{
  "schema": "almanac-concordance/v1",
  "edition": "almanacA0a — the centre of the even hybrid family quantum GL1 (PILOT)",
  "sandbox": "SandboxA/sandboxA0a",
  "goal": "center-GL1 (gl1_center_newton)",
  "frozen_at": null,
  "frozen_note": "ROWS FREEZE AT DEPOSIT (manifest §9), and deposit is sequenced AFTER instrument item 2 lands — the fresh enumerated-cone release_verify log — so the edition's certification citation meets complete evidence (condition 1 of the acceptance, adopting this edition's own stated preference). The F-E1 disclosure stands until then. Drift protocol: when record bytes move, the tree owner mails the Editor, who re-hashes and re-gates before deposit.",
  "assembled_utc": "2026-08-13",
  "assembled_by": "the Almanac Editor (AD-27)",
  "how_to_read_the_warrant_field": {
    "the_three_warrants": "INK, ORANGE, BLUE — in that order, which is the mark's order and the order they are named in everywhere else. They are KINDS of warrant, not levels of one: the argument a person refereed is not the weak version of the proof a machine checked.",
    "ink": "THE INK WARRANT. An argument written out for a human reader and refereed. The row pins it to a hashed document at a named location, so a reader can check they are reading the bytes the row cites; its ancestry was refereed at source, per row; and the proof itself was read by an independent adversarial referee, recorded at edition level. This is a warrant, not the absence of one — a refereed informal proof is what the other two are checked against. WHAT IT DOES NOT YET CARRY, stated because the other two warrants do carry it: a per-row record of WHO refereed THIS claim and when. Refereeing of the sources is per row; refereeing of the argument is recorded for the edition. Neither is yet a per-claim anchor.",
    "orange": "THE ORANGE WARRANT. Verified by computation over the bound in declared_range, and over nothing else. The bound is part of the claim.",
    "blue": "THE BLUE WARRANT. A Lean declaration states THIS ROW'S claim and its #print axioms result is exactly the clean triple with no sorryAx. The axioms field is the ACTUAL measured result, never a restatement of the sandbox's closed status.",
    "the_rule_that_matters": "warrant describes THIS ROW, not the sandbox. sandboxA0a is closed with a clean axiom triple; that does not make every row the blue warrant. A row whose Lean declaration is absent is not blue-warranted however completely the sandbox is certified.",
    "and_the_one_that_matters_more": "A row may not carry the blue warrant on the strength of a Lean proof if the claim the row makes is about the CODE. See EMBEDDING_NOTE.md §5. The Lean declaration certifies the Lean statement. Nothing else."
  },
  "measurement_provenance": {
    "axioms_measured_by": "mcp lean-lsp lean_verify (read-only; writes nothing), 2026-08-13, by the Editor directly and by a delegated read-only agent",
    "why_not_release_verify": "release_verify.sh --source is NOT the Editor's act — certification belongs to the tree owner (charter amended 2026-08-13 on this edition's finding F-E2). The Editor CITES the sandbox's existing closure certification and establishes each row's axioms READ-ONLY, so every 'axioms' array below is a first-hand lean_verify result rather than a quotation. NOTE the interaction with F-E1: the cited closure certification currently rests on incomplete evidence, and its repair is a separate act on the Overseer's desk.",
    "toolchain": "leanprover/lean4:v4.30.0, Mathlib c5ea00351c28e24afc9f0f84379aa41082b1188f",
    "estate_commit": "a4c04990",
    "julia_battery": "measured 2026-08-13 under engine/job_gate.py medium: 87/87 PASS (Oscar 1.8.0, julia 1.12.6)"
  },
  "rows": [
    {
      "id": "A0a-01-clause-i",
      "informal": {
        "statement": "U^ev = N^ev is an A_t-subalgebra of U.",
        "file": "informal/proofv0a.tex",
        "sha256": "bbd6f055bd5aff614d1a6575b24949d8fd2b805ebda20e33e5c706f28713bbae",
        "label": "Proposition (clause i), line 111"
      },
      "cas": {
        "object": "az / newton — closure of grid-integrality under products",
        "package": "GL1Newton",
        "version": "0.1.0",
        "ledger_claim": "A1.closure-products"
      },
      "lean": {
        "declaration": "HybridQuantumLean.A1.GL1Newton.clause_i",
        "file": "Sandbox/A1/GL1/GOALv0a.lean",
        "sha256": "3db277a957cb02a8132502e3286a6c0073d6538852165fec735af1a56a57b540",
        "also": [
          "HybridQuantumLean.A1.GL1Newton.clause_i_ambient (the 'subalgebra OF U' reading, taken literally)",
          "HybridQuantumLean.A1.GL1Newton.clause_i_in_torus (the even embedding is injective)",
          "HybridQuantumLean.A1.GL1Newton.KzBridge.clause_i_Kz (the same over the K_z model)"
        ]
      },
      "literature": [
        "quantum integer-valued polynomials form a ring (Harman–Hopkins §1)"
      ],
      "convention_frame": "Current Sandbox symbols: q = v^2, t = z^2; A_t = Z[v^{±1}, t^{±1}]; F_t = Q(v)[t^{±1}]; Y̌ = (T^+)^2 with ev_χ(Y̌) = q^χ, unshifted and t-free. NOTE the Lean sources predate the 2026-08-10 migration and are written in the LEGACY symbols (A_z, Q = q^2, z): the Lean 'A_z' IS this row's A_t and the Lean 'Q' IS this row's q. Restated by the edition; the sources were not migrated.",
      "ancestry": "lit-harman-q-polya-qbinomial-basis — REFEREED AND CONFIRMED 2026-08-13 from the arXiv source with re-derived probes (the single-pass caveat F-A1 is DISCHARGED). Card written in retired notation; frame restated by the edition (ANCESTRY.md §3.1).",
      "warrant": "blue",
      "axioms": [
        "propext",
        "Classical.choice",
        "Quot.sound"
      ],
      "notes": "Measured by the Editor 2026-08-13, clean triple, no sorryAx. The proof is the elementary one — N^ev is an intersection of preimages ev_χ^{-1}(A_t) of a subring under ring homomorphisms — and does not depend on the Harman–Hopkins content; the citation is ancestry for the IDEA, not a dependency.",
      "ancestry_print": "Harman–Hopkins §1 — see Sources.",
      "evidence_anchor": "informal/proofv0a.ledger.json, claim A1.closure-products, with receipts in proofv0a.ledger.cas_receipts.md"
    },
    {
      "id": "A0a-02-clause-ii",
      "informal": {
        "statement": "The Harish–Chandra projection restricts to an isomorphism of A_t-algebras HC : Z(U^ev) → (N^ev)^W, and this isomorphism is the identity map of N^ev.",
        "file": "informal/proofv0a.tex",
        "sha256": "bbd6f055bd5aff614d1a6575b24949d8fd2b805ebda20e33e5c706f28713bbae",
        "label": "Proposition (clause ii), line 134"
      },
      "cas": {
        "object": null,
        "package": null,
        "version": null,
        "note": "No computational claim. U is commutative because Φ = ∅, so HC = id and W is trivial; the content is definitional unwinding, not computation. The ledger records this step as prose (step:clause-ii), and the edition does not manufacture a CAS object to fill the column."
      },
      "lean": {
        "declaration": "HybridQuantumLean.A1.GL1Newton.clause_ii",
        "file": "Sandbox/A1/GL1/GOALv0a.lean",
        "sha256": "3db277a957cb02a8132502e3286a6c0073d6538852165fec735af1a56a57b540",
        "also": [
          "HybridQuantumLean.A1.GL1Newton.clause_ii_ambient (Def 3 read literally: the centre taken after base change)",
          "HybridQuantumLean.A1.GL1Newton.ZUev_eq_ZUevAmbient (the two readings of Def 3 coincide — PROVED)"
        ]
      },
      "literature": [
        "De Concini–Procesi, Quantum Groups, LNM 1565 §18.3 (generic quantum Harish–Chandra isomorphism)",
        "Jantzen, Lectures on Quantum Groups, GSM 6, THEOREM 6.25 (never §6.6, which is containment only)",
        "the GL2 in-programme predecessor"
      ],
      "convention_frame": "As row 01. Three frames must be kept apart and this is the row where they collide: (a) De Concini–Procesi carry the ρ-shift in the map γ and land in k[2P]^W — TWICE the weight lattice — over k(q) with NO integral form and NO family parameter; (b) the programme carries the shift in the COORDINATES; (c) the GL2 card's two-frame trap — N^ev is Newton in the UNSHIFTED Y̌_i = (T_i^+)^2 while s_1-invariance is natural in the SHIFTED coordinates, and ν_d(Y_shifted) seeds are NOT valid inputs. At GL1 the Weyl group is trivial so the invariance condition is VACUOUS; the row is therefore degenerate and proves nothing about higher rank.",
      "ancestry": "gl2-hc-image-theorem (ours, the in-programme predecessor the manuscript actually cites) PLUS lit-dcp-generic-harish-chandra-isomorphism and lit-jantzen-harish-chandra-even-torus (the literature ancestors, located 2026-08-10 after the manuscript closed). THE MANUSCRIPT ITSELF CITES ONLY THE FIRST — the edition's ancestry is richer than the manuscript's citation, and states the difference explicitly (ANCESTRY.md §4).",
      "warrant": "blue",
      "axioms": [
        "propext",
        "Classical.choice",
        "Quot.sound"
      ],
      "notes": "Measured by the Editor 2026-08-13, clean triple. TWO limits a reader must carry: (1) the predecessor card gl2-hc-image-theorem records '✅ FULLY CERTIFIED' AND, in the same field, 'NOT yet: abstract U_A form + necessity/⊆ (λ-transcendence layer), two-variable even-grid bridge' — the tick and the limit travel together; (2) this row is the Φ = ∅ degeneration, where the theorem is nearly trivial. Its value is that it pins the GL1 case of a statement whose rank ≥ 2 cases are the open frontier — not that it is hard.",
      "ancestry_print": "The GL₂ predecessor in this programme, with De Concini–Procesi §18.3 and Jantzen Thm 6.25 as the literature ancestors — see Sources. The manuscript itself cites only the first."
    },
    {
      "id": "A0a-03-clause-iii",
      "informal": {
        "statement": "N^ev = S = Σ_{u∈Z} Σ_{r≥0} A_t · Y̌^u ν_r(Y̌) — the even Newton lattice is exactly the A_t-span of the shifted divided classes.",
        "file": "informal/proofv0a.tex",
        "sha256": "bbd6f055bd5aff614d1a6575b24949d8fd2b805ebda20e33e5c706f28713bbae",
        "label": "Theorem (thm:iii), line 181"
      },
      "cas": {
        "object": "newton vs mem_span — agreement of the evaluation-defined predicate with the span-defined predicate",
        "package": "GL1Newton",
        "version": "0.1.0",
        "referee_pin": "n1_clause3_referee_pin.jl/.out"
      },
      "lean": {
        "declaration": "HybridQuantumLean.A1.GL1Newton.Nev_eq_span",
        "file": "Sandbox/A1/GL1/NewtonUnivSpan.lean",
        "sha256": "1d1a1e50e95363b522e7c7368d7b1bb9027c1bd61cb8087f6d99af56d1652211",
        "also": [
          "HybridQuantumLean.A1.GL1Newton.Newton_iff_mem_span (iff form)",
          "HybridQuantumLean.A1.GL1Newton.mem_span_of_Newton (the substantive leg)",
          "HybridQuantumLean.A1.GL1Newton.clause_iii (bundle form)",
          "HybridQuantumLean.A1.GL1Newton.KzBridge.clause_iii_Kz (over the K_z model)"
        ]
      },
      "literature": [
        "Harman–Hopkins, Quantum integer-valued polynomials, arXiv:1601.06110, §1 (quantum Pólya basis) and §4 (bilateral localization)"
      ],
      "convention_frame": "As row 01, PLUS the transport that makes the citation apply at all. Their grid is ADDITIVE (integrality imposed at the q-integers x = [n]_q); ours is MULTIPLICATIVE (Y̌ = q^m). The two are exchanged by the node-preserving substitution Y̌ = 1 + (q−1)x, which is invertible over Q(q) but not over Z[q^{±1}], so it does NOT map Z[q^{±1}][x] into Z[q^{±1}][Y̌]. Because integrality is imposed AT THE NODES and the nodes correspond, the substitution nevertheless carries their lattice ISOMORPHICALLY onto ours, taking each of their basis elements to nu_k(Y̌) term by term. (Corrected 2026-08-13: this edition previously denied it was a lattice isomorphism, which was false — the transport is legitimate precisely because it is one; what fails is only the naive map of coefficient lattices.) Their Gaussian binomial is ONE-SIDED (differs from the symmetric convention by a unit power of q: integrality survives, explicit coefficients do not). Their §1 works over Z[q], a PROPER subring of A_t; the bilateral statement needed here is §4, where the localization inverts q ONLY — not t, not cyclotomic factors. NAME COLLISION, and the migration made it worse: their z is our Y̌; our free parameter is t; today's letter z is the square root of t.",
      "ancestry": "lit-harman-q-polya-qbinomial-basis (refereed and CONFIRMED 2026-08-13; F-A1 DISCHARGED — C1 referee pass run 2026-08-13, both cards CONFIRMED with no correction from the arXiv LaTeX source with re-derived probes; report corpus/reports/HARMAN-HOPKINS-C1-REFEREE-PASS-2026-08-13.md. TWO LIMITS SURVIVE, properties of the source not defects: the lattice-FREENESS probe is unrun (two-way integrality does not give equality of lattices), and the Lusztig-Cartan-form sentence stays an unproved remark, grade literature-remark) + lit-harman-bilateral-q-integer-localization (the pre-existing 2026-07-16 card, NOT under that caveat). The manuscript transports the argument; it does not import the theorem.",
      "warrant": "blue",
      "axioms": [
        "propext",
        "Classical.choice",
        "Quot.sound"
      ],
      "notes": "Measured by the Editor 2026-08-13, clean triple. This is the substantive theorem of the sandbox. TWO things the edition will not let a reader conflate: (1) it must NOT be read as 'the Harman–Hopkins lattice IS our Newton lattice' — the four-way lattice reconciliation T^Lus = N = T_WN = T_HH is OPEN on the shelf (F-A3); (2) the finite degree d is ESSENTIAL to the §4 integrality test, which is what licenses the manuscript's WINDOWED reverse inclusion — that is load-bearing, not a convenience. Non-vacuity is separately proved: see row 08. SPAN, NOT BASIS, AND IT CANNOT BE UPGRADED: the generating family is provably NOT independent — from nu_1(X) = (X−1)/(q−1) one gets the A_t-relation (q−1)·nu_1(Ycheck) − Ycheck·nu_0 + nu_0 = 0. Harman-Hopkins prove FREE generation over Z[q]; clause (iii) asserts only equality of a lattice with a span, which is the correct and weaker form. 'Basis', 'free module' and 'freely generated' must never be written beside this row. What remains open is whether N^ev is free over A_t on some OTHER family — not whether this one is free, which is settled in the negative.",
      "ancestry_print": "Harman–Hopkins §§1 and 4; Gramain Prop. 2.2 for the classical multiplicative-grid statement — see Sources.",
      "evidence_anchor": "n1_clause3_referee_pin.out for the independent agreement check; ledger claims via informal/proofv0a.ledger.json"
    },
    {
      "id": "A0a-04-lemma-grid",
      "informal": {
        "statement": "For all m ∈ Z and r ≥ 0, B_r(m) = ν_r(q^m) ∈ Z[q^{±1}] — the grid values of the divided classes are integral, including at negative nodes.",
        "file": "informal/proofv0a.tex",
        "sha256": "bbd6f055bd5aff614d1a6575b24949d8fd2b805ebda20e33e5c706f28713bbae",
        "label": "Lemma (lem:grid), line 194"
      },
      "cas": {
        "object": "nu_grid + az — integrality of ν_r(q^χ) on the bilateral grid",
        "package": "GL1Newton",
        "version": "0.1.0",
        "ledger_claims": [
          "G1.grid.vanishing",
          "G2.grid.gaussian-integral",
          "G3.grid.reflection-integral"
        ]
      },
      "lean": {
        "declaration": "HybridQuantumLean.A1.GL1Newton.Az_nuGrid",
        "file": "Sandbox/A1/GL1/NewtonUnivGrid.lean",
        "sha256": "4ab6656818b57967fdd90de98ba214e0f792b1a103a63215600534217d483599"
      },
      "literature": [
        "Harman–Hopkins §1 (Gaussian-binomial value pattern), extended to negative nodes as their §4 bilateral localization requires"
      ],
      "convention_frame": "As row 03. The one-sided Gaussian convention is what the grid values are expressed in; the basis denominator q^{binom(k,2)}[k]_q! is where a normalisation error would hide, which is why it was probed on the oracle (49/49 over 0 ≤ n,k ≤ 6).",
      "ancestry": "lit-harman-q-polya-qbinomial-basis (refereed and CONFIRMED 2026-08-13; F-A1 DISCHARGED — C1 referee pass run 2026-08-13, both cards CONFIRMED with no correction from the arXiv LaTeX source with re-derived probes; report corpus/reports/HARMAN-HOPKINS-C1-REFEREE-PASS-2026-08-13.md. TWO LIMITS SURVIVE, properties of the source not defects: the lattice-FREENESS probe is unrun (two-way integrality does not give equality of lattices), and the Lusztig-Cartan-form sentence stays an unproved remark, grade literature-remark) + the programme companion card even-newton-gaussian-grid-values. THE COMPANION CARD IS CITED FOR FORWARD GRID-INTEGRALITY ONLY: its stronger sentence — that the even-generated span EQUALS the Verma-saturated Newton lattice — is REFUTED (even-gaussian-span-not-newton-lattice-refuted), CORRECTED 2026-08-13, the printed witness was FALSE in this frame: nu_1(q^3) = q^2+q+1 IS integral. The true witness sits on the ODD grid — nu_1(v^3) = (v^2+v+1)/(v+1) is NOT in A_t — which is precisely why the goal reads 'even'. Verified on the CAS kernel, identity sha256 0f8f7d63dd6a37e4886d7cbb71edfc9e1f503705e3354bb52f25692f676eb64d. The false form was transported from the card, whose own frame is the RETIRED notation where its q is today's v; restating it without migrating the symbol is the inverted-dictionary defect recurring. Forward integrality on a grid never implies saturation of the lattice. CLASSICAL ANCESTOR NOW HELD (2026-08-13): Gramain, LNM 1415, §2 Prop 2.2, p. 124 — the Gauss binomial polynomials generating the multiplicative-grid integer-valued module; our nu_r IS his G_r exactly. CORRECTED 2026-08-13 (reverse pass): Gramain's printed exponent is NEGATIVE — he DIVIDES by q^{n(n-1)/2} where this edition first read him as multiplying. So G_n = nu_n EXACTLY: his normalization IS ours, not ours up to a unit. SETTLED FROM THE PAGE'S OWN CONTENT, independent of the glyph: p.125 states 'On voit que G_n(q^n) = 1', and nu_n(q^n) = 1 by construction, so the exponent MUST be negative — a positive one would give G_n(q^n) = q^{n(n-1)}. WITHDRAWN: the earlier claim 'G_n = q^{n(n-1)} * nu_n' and its CAS certificate b058e9158de16756c6f9fe4f2a9660f74402f0fea850bd3602aa46e225236e04. The certificate is not false — it faithfully certifies the identity for the formula that was TYPED INTO IT, which carried a dropped minus. A MACHINE CERTIFICATE CERTIFIES ITS INPUT, NOT THE SOURCE. See gaps/GAPS.md F-A6. The correction makes this row STRONGER: exact coincidence of normalizations, not agreement up to a unit. This upgrades the divided classes' ancestry from a q-deformed analogue to a classical statement on our own grid. CARD: lit-gramain-geometric-progression-integer-valued-basis. CITE BY ARTICLE, NEVER BY VOLUME (trap found by the Librarian, 2026-08-13): LNM 1415 is a VOLUME whose articles number independently, and a naive search for 'Proposition 2.2' in it lands FIRST on a different article's statement about primes p^k dividing a binomial-type coefficient. The citation must read 'Gramain, LNM 1415, Prop 2.2, p. 124' — never 'LNM 1415 Prop 2.2'. ANCESTRY.md §8.6.",
      "warrant": "blue",
      "axioms": [
        "propext",
        "Classical.choice",
        "Quot.sound"
      ],
      "notes": "Certified via the parent A1 machinery (CenterNewtonZ.nuNewton_zpow_grid_mem), consumed rather than reproved. Independently corroborated over a declared range: ledger claims G1 (0≤m<r≤8), G2 (0≤r≤m≤10), G3 (1≤n≤5, 0≤r≤5), plus battery sweep r ∈ 0..8 × χ ∈ −9..9 = 171 cases, all integral, measured 87/87 PASS on 2026-08-13. The theorem is unbounded; the computations are not, and the edition does not let the second stand in for the first.",
      "ancestry_print": "Harman–Hopkins §1; Gramain Prop. 2.2, whose Gauss binomials are exactly these divided classes — see Sources.",
      "evidence_anchor": "informal/proofv0a.ledger.json, claims G1–G3, with receipts in proofv0a.ledger.cas_receipts.md"
    },
    {
      "id": "A0a-05-lemma-fwd",
      "informal": {
        "statement": "For every u ∈ Z and r ≥ 0, Y̌^u ν_r(Y̌) ∈ N^ev; hence S ⊆ N^ev.",
        "file": "informal/proofv0a.tex",
        "sha256": "bbd6f055bd5aff614d1a6575b24949d8fd2b805ebda20e33e5c706f28713bbae",
        "label": "Lemma (lem:fwd), line 254"
      },
      "cas": {
        "object": "newton on nuGen witnesses",
        "package": "GL1Newton",
        "version": "0.1.0",
        "ledger_claims": [
          "F1.module-scalar-bridge",
          "F2.shifted-generator-evaluation",
          "F3.generator-values-integral"
        ]
      },
      "lean": {
        "declaration": "HybridQuantumLean.A1.GL1Newton.Newton_nuGen",
        "file": "Sandbox/A1/GL1/NewtonUnivGrid.lean",
        "sha256": "4ab6656818b57967fdd90de98ba214e0f792b1a103a63215600534217d483599",
        "also": [
          "HybridQuantumLean.A1.GL1Newton.Newton_of_mem_span (the full easy leg)"
        ]
      },
      "literature": [
        "Harman–Hopkins §1 — the transported forward half: q-binomials are quantum integer-valued"
      ],
      "convention_frame": "As row 03.",
      "ancestry": "lit-harman-q-polya-qbinomial-basis (refereed and CONFIRMED 2026-08-13; F-A1 DISCHARGED — C1 referee pass run 2026-08-13, both cards CONFIRMED with no correction from the arXiv LaTeX source with re-derived probes; report corpus/reports/HARMAN-HOPKINS-C1-REFEREE-PASS-2026-08-13.md. TWO LIMITS SURVIVE, properties of the source not defects: the lattice-FREENESS probe is unrun (two-way integrality does not give equality of lattices), and the Lusztig-Cartan-form sentence stays an unproved remark, grade literature-remark).",
      "warrant": "blue",
      "axioms": [
        "propext",
        "Classical.choice",
        "Quot.sound"
      ],
      "notes": "The easy leg of clause (iii). Corroborated over declared ranges −2≤u≤2, 0≤r≤4, −3≤m≤4 (ledger F2/F3), with a control (control.coefficientwise-coarsening at r=2) that must and does REFUTE.",
      "ancestry_print": "Harman–Hopkins §1 — see Sources.",
      "evidence_anchor": "informal/proofv0a.ledger.json, claims F1–F3, with receipts in proofv0a.ledger.cas_receipts.md"
    },
    {
      "id": "A0a-06-lemma-rev",
      "informal": {
        "statement": "If g ∈ N^ev is an even toral POLYNOMIAL of degree ≤ d, then g = Σ_{r≤d} c_r ν_r(Y̌) with all c_r ∈ A_t. The windowed reverse inclusion.",
        "file": "informal/proofv0a.tex",
        "sha256": "bbd6f055bd5aff614d1a6575b24949d8fd2b805ebda20e33e5c706f28713bbae",
        "label": "Lemma (lem:rev), line 276"
      },
      "cas": {
        "object": "expand — the triangular Newton-coordinate sweep",
        "package": "GL1Newton",
        "version": "0.1.0",
        "ledger_claims": [
          "R1.unitriangular-det",
          "R2.inverse-integral"
        ]
      },
      "lean": {
        "declaration": "HybridQuantumLean.A1.GL1Newton.mem_span_of_Newton",
        "file": "Sandbox/A1/GL1/NewtonUnivSpan.lean",
        "sha256": "1d1a1e50e95363b522e7c7368d7b1bb9027c1bd61cb8087f6d99af56d1652211",
        "also": [
          "HybridQuantumLean.A1.GL1Newton.expand (the coordinate map)",
          "HybridQuantumLean.A1.GL1Newton.expand_spec",
          "HybridQuantumLean.A1.GL1Newton.expand_witnesses_span"
        ]
      },
      "literature": [
        "Pólya's windowed-interpolation argument as q-deformed in Harman–Hopkins §1 (interpolation proof, printed pp. 3–4), run on the multiplicative grid with t a spectator"
      ],
      "convention_frame": "As row 03, and THE FINITE DEGREE d IS ESSENTIAL — Harman–Hopkins Lemma 4.2 tests integrality at nodes 0..d and concludes for all of Z. The window is a hypothesis of the source, not an artefact of our proof.",
      "ancestry": "lit-harman-q-polya-qbinomial-basis (refereed and CONFIRMED 2026-08-13; F-A1 DISCHARGED — C1 referee pass run 2026-08-13, both cards CONFIRMED with no correction from the arXiv LaTeX source with re-derived probes; report corpus/reports/HARMAN-HOPKINS-C1-REFEREE-PASS-2026-08-13.md. TWO LIMITS SURVIVE, properties of the source not defects: the lattice-FREENESS probe is unrun (two-way integrality does not give equality of lattices), and the Lusztig-Cartan-form sentence stays an unproved remark, grade literature-remark) + lit-harman-bilateral-q-integer-localization (refereed status: pre-existing 07-16 card).",
      "warrant": "blue",
      "axioms": [
        "propext",
        "Classical.choice",
        "Quot.sound"
      ],
      "notes": "The substantive leg. The Lean 'expand' was introduced to close a faithfulness finding and is re-verified non-circular (it never mentions span, Newton or nuGenSet). Corroborated at window size d = 8 (ledger R1/R2), with control.offdiagonal-not-one at (3,2) refuting as required. CAVEAT for the embedding: whether the Julia expand's truncation parameter D agrees with the Lean expand has NEVER been examined (gap G2).",
      "ancestry_print": "Pólya's windowed interpolation as q-deformed in Harman–Hopkins §1; the finite degree is essential to the test — see Sources.",
      "evidence_anchor": "informal/proofv0a.ledger.json, claims R1–R2, with receipts in proofv0a.ledger.cas_receipts.md"
    },
    {
      "id": "A0a-07-definition-1-presented",
      "informal": {
        "statement": "U is the F_t-algebra on invertible pairwise commuting K_{n,±} with K_{0,±}=1, K_{m+n,±}=K_{m,±}K_{n,±}, K_{n,+}K_{n,−}=t^n; and the monomials (T^+)^w, w ∈ Z, form an F_t-basis.",
        "file": "informal/goalv0a.tex",
        "sha256": "cfc52b10830f94dfa24718547c3282070b71ceed36ae2d0304ca49b203fcbeaf",
        "label": "Definition 1 (def:U)"
      },
      "cas": {
        "object": null,
        "package": null,
        "version": null,
        "note": "No computational claim; this is a presentation."
      },
      "lean": {
        "declaration": "HybridQuantumLean.A1.GL1Newton.Presentation.equivTorus",
        "file": "Sandbox/A1/GL1/PresentedU.lean",
        "sha256": "5a5a7e68e8da1479efaf89ce3bfcb8eb4b412a70b4f969a7305f9e5e333b74d4",
        "also": [
          "HybridQuantumLean.A1.GL1Newton.Presentation.uBasis (the basis assertion, PROVED)",
          "HybridQuantumLean.A1.GL1Newton.Presentation.existsUnique_lift (the universal property)",
          "HybridQuantumLean.A1.GL1Newton.Presentation.modelEquiv"
        ]
      },
      "literature": [],
      "convention_frame": "Split torus, z_i free, unshifted Verma — the programme-wide convention. The presented algebra is a quotient of the group algebra K[Z × Z] by the SINGLE remaining relation K_{1,+}K_{1,−} = t; the full family K_{n,+}K_{n,−} = t^n is DERIVED, not imposed.",
      "ancestry": "SPLIT, and the split is the finding (edition-level search, 2026-08-13). PRESENTATION HALF — PREDECESSOR LOCATED: Lusztig, Introduction to Quantum Groups, Proposition 3.2.4, via card lit-lusztig-triangular-decomposition-toral-freeness. The algebra on invertible commuting generators indexed additively by a lattice, identified with that lattice's group algebra. CITE THE PARENTHESIS: the freeness on {K_mu} is stated in Lusztig's parenthetical '(This is the group algebra of Y over Q(v).)', not in the displayed statement — a citation omitting it supports a presentation but not a basis. FAMILY-PARAMETER HALF — NONE LOCATED: no predecessor anywhere on the shelf for the second leg K_{n,-} together with an adjoined free invertible t satisfying K_{1,+}K_{1,-} = t. This is a POSITIVE absence, not a silent zero-hit: three independent cards assert it as a frame fact (lit-dcp-generic-harish-chandra-isomorphism 'no family parameter'; lit-dcp-verma-contravariant-shapovalov 'no family parameter'; the Losev-Tsymbaliuk-Vu transcript 'no central group-like z_a'). Nearest structural neighbour, and NOT a predecessor: Lacabanne's double Cartan, whose second parameter is the QUOTIENT z_i = K_i L_i^{-1}, a central root-torus variable, not an adjoined free one. Our own predecessor for this half is ours: the internal note own-habiro-le-even-hybrid-centers-explicit-torus §2, with the registry entry objects/gl4.coordinate-split-torus — both pinned by this edition's manifest and NOT distributed with it (they carry the programme's general conjecture, which is work in preparation). SEARCH OF RECORD: queries 'group algebra of the weight lattice torus Laurent Cartan part K_i invertible' (0), 'hybrid family torus' (0), 'K_n^+ K_n^-' (0), 'hybrid torus' (11), 'Cartan part' (30), 'split torus' (6), 'z_i = K_{i,+}K_{i,-}' (0), 'group algebra' (10), 'central group-like z_a' (0), 'family parameter' (9), 'generators and relations' (33); statements + objects shelves; 2026-08-13. No acquisition warranted — the absence is structural, not a gap in holdings.",
      "warrant": "blue",
      "axioms": [
        "propext",
        "Classical.choice",
        "Quot.sound"
      ],
      "notes": "This row is why the goal bundle grew from four fields to eight. Wave 2 ASSUMED the presented algebra was the Laurent torus; wave 3 PROVED it (equivTorus), closing finding F1. The universal property is established for commutative target algebras only — recorded on the record as verification finding N2, not a sorry.",
      "ancestry_print": "Lusztig, Introduction to Quantum Groups, Prop. 3.2.4 with its parenthesis, for the lattice-group-algebra presentation. No predecessor is located for the adjoined free parameter; three independent cards record its absence."
    },
    {
      "id": "A0a-08-nondegeneracy",
      "informal": {
        "statement": "Clause (iii) is not vacuously true of a degenerate object: A_t[Ycheck^{±1}] ⊊ N^ev ⊊ K_1[Ycheck^{±1}] — strictly, on both sides, with K_1 = Frac(A_t) the ambient the certified declaration actually uses.",
        "file": null,
        "sha256": null,
        "label": "Proved in the formal development; the manuscript states no counterpart."
      },
      "cas": {
        "object": "the separating witness: nu_1 is grid-integral and in the span, and is not Laurent",
        "package": "GL1Newton",
        "version": "0.1.0",
        "note": "battery test set A4/H1; also the separator lane of the N1 referee pin"
      },
      "lean": {
        "declaration": "HybridQuantumLean.A1.GL1Newton.clause_iii_nondegenerate",
        "file": "Sandbox/A1/GL1/NonDegeneracy.lean",
        "sha256": "69160c8b53a5c260d7d7754d2d8f2cc4dd3d4e55bdce1f336a62b7487e976835",
        "also": [
          "HybridQuantumLean.A1.GL1Newton.trap4_separator (ν_1(Y̌) is in N^ev but not Laurent)",
          "HybridQuantumLean.A1.GL1Newton.FamilyField1.Qsub_one_inv_not_mem ((q−1)^{-1} ∉ A_t — the one arithmetic input)",
          "HybridQuantumLean.A1.GL1Newton.Newton_ssubset_univ (the ceiling)",
          "HybridQuantumLean.A1.GL1Newton.nuGenSpan_ne_top (the span is not everything)",
          "HybridQuantumLean.A1.GL1Newton.Laurent_ssubset_Newton (the floor)"
        ]
      },
      "literature": [],
      "convention_frame": "As row 01. The separator is ν_1(Y̌) = (Y̌ − 1)/(q − 1), whose Y̌-coefficient (q−1)^{-1} escapes A_t while all its GRID values stay integral — which is exactly why the Newton lattice is strictly larger than the Laurent ring and the divided classes are genuinely needed.",
      "ancestry": "PREDECESSORS LOCATED, in three layers, with one caution (edition-level search, 2026-08-13). CLASSICAL: Polya 1919, via the held transcript harman-hopkins-quantum-integer-valued-polynomials, Proposition 1.1 — 'R is freely generated as an abelian group by the binomial polynomials binom(x,k)'. NOTE THE LOGICAL GAP AND DO NOT CLOSE IT SILENTLY: the source states a BASIS, not a strict inclusion. Strictness follows immediately (binom(x,2) is integer-valued and not in Z[x]), so the honest phrasing is \"Polya's basis theorem, from which the strict containment is immediate\", NEVER \"Polya proved the strict containment\". q-ANALOGUE: Harman-Hopkins §1 Props 1.1-1.2 via lit-harman-q-polya-qbinomial-basis (refereed and CONFIRMED 2026-08-13 from the arXiv source with re-derived probes; F-A1 DISCHARGED — C1 referee pass run 2026-08-13, both cards CONFIRMED with no correction from the arXiv LaTeX source with re-derived probes; report corpus/reports/HARMAN-HOPKINS-C1-REFEREE-PASS-2026-08-13.md. TWO LIMITS SURVIVE, properties of the source not defects: the lattice-FREENESS probe is unrun (two-way integrality does not give equality of lattices), and the Lusztig-Cartan-form sentence stays an unproved remark, grade literature-remark), frame: one variable, ADDITIVE grid, coefficient ring Z[q] or Z[q^{±1}], NO free parameter. OUR OWN, FOR THE WITNESS ONLY: even-gaussian-span-not-newton-lattice-refuted displays the identical separating element nu_1(Ycheck) = (Ycheck-1)/(q-1) and proves a strict inclusion — BUT OF A DIFFERENT PAIR BY A DIFFERENT MECHANISM (it separates the Gaussian-generator span from the Newton lattice via a finer-vs-coarser grid; this row separates A_t[Ycheck^{±1}] from N^ev via a non-unit coefficient (q-1)^{-1}). Predecessor for the witness; NOT for this inclusion. ACQUISITION PARTLY FULFILLED — see below. STILL WANTED: Cahen-Chabert, Integer-Valued Polynomials, AMS Surveys 48 (1997) — the standard reference, cited by our own held source, NOT on our shelf; also Polya 1915 original and Gramain 1990. Until held, the classical statement is reachable only THROUGH a quotation inside another paper, and the edition says so rather than citing what it does not hold. ACQUISITION FULFILLED 2026-08-13: Gramain LNM 1415 is now HELD (conference volume 'Cinquante Ans de Polynomes'), and its §2 PROPOSITION 2.2, printed p. 124, is the classical MULTIPLICATIVE-GRID ancestor: the polynomials P with P(q^k) in Z for all k form the Z-module generated by the Gauss binomial polynomials G_n. CORRECTED 2026-08-13 (reverse pass): Gramain's printed exponent is NEGATIVE — he DIVIDES by q^{n(n-1)/2} where this edition first read him as multiplying. So G_n = nu_n EXACTLY: his normalization IS ours, not ours up to a unit. SETTLED FROM THE PAGE'S OWN CONTENT, independent of the glyph: p.125 states 'On voit que G_n(q^n) = 1', and nu_n(q^n) = 1 by construction, so the exponent MUST be negative — a positive one would give G_n(q^n) = q^{n(n-1)}. WITHDRAWN: the earlier claim 'G_n = q^{n(n-1)} * nu_n' and its CAS certificate b058e9158de16756c6f9fe4f2a9660f74402f0fea850bd3602aa46e225236e04. The certificate is not false — it faithfully certifies the identity for the formula that was TYPED INTO IT, which carried a dropped minus. A MACHINE CERTIFICATE CERTIFIES ITS INPUT, NOT THE SOURCE. See gaps/GAPS.md F-A6. The correction makes this row STRONGER: exact coincidence of normalizations, not agreement up to a unit. FRAME: Gramain's q is a NATURAL NUMBER >= 2 over coefficient ring Z, ours an indeterminate over A_t — so q^{n(n-1)} is a unit for us and not for him; ancestor of the FORM, not a citable instance of our statement. CARD: lit-gramain-geometric-progression-integer-valued-basis (Librarian, 2026-08-13, read at source). CITE BY ARTICLE, NEVER BY VOLUME (trap found by the Librarian, 2026-08-13): LNM 1415 is a VOLUME whose articles number independently, and a naive search for 'Proposition 2.2' in it lands FIRST on a different article's statement about primes p^k dividing a binomial-type coefficient. The citation must read 'Gramain, LNM 1415, Prop 2.2, p. 124' — never 'LNM 1415 Prop 2.2'. See ANCESTRY.md §8.6.",
      "warrant": "blue",
      "axioms": [
        "propext",
        "Classical.choice",
        "Quot.sound"
      ],
      "notes": "Measured first-hand 2026-08-13: the clean axiom base on the main declaration and on each of the five listed beside it. This row corrects a stale record: the source manifest of 2026-07-21 still carries finding F7 declaring these witnesses absent from the delivered cone and present only in a scratch tree /tmp/v0averify/. They are IN-TREE (NonDegeneracy.lean, committed 2026-07-20 — a day BEFORE the manifest that declares them missing), imported at Sandbox.lean:120, tracked in git, and clean. The scratch tree no longer exists. See F-E3. Three of the four witnesses named in the older record carry different identifiers in the delivered sources.",
      "ancestry_print": "Pólya's basis theorem, from which strictness is immediate; the q-analogue in Harman–Hopkins §1 — see Sources. The separating element is this programme's own.",
      "evidence_anchor": "almanac/GL1Newton/test/runtests.jl, the separation tests; the odd-node witness is verified at CAS identity 0f8f7d63dd6a37e4886d7cbb71edfc9e1f503705e3354bb52f25692f676eb64d"
    },
    {
      "id": "A0a-09-kz-bridge",
      "informal": {
        "statement": "Enlarging the ambient coefficient RING from F_t = Q(v)[t^{±1}] (not a field) to K_1 = Frac(A_t) = Q(v,t) adds no new Newton elements: the two readings cut out the same set.",
        "file": null,
        "sha256": null,
        "label": "Proved in the formal development; the manuscript states no counterpart."
      },
      "cas": {
        "object": null,
        "package": null,
        "version": null,
        "note": "No computational claim; a ring-theoretic containment argument."
      },
      "lean": {
        "declaration": "HybridQuantumLean.A1.GL1Newton.KzBridge.Newton_mem_KzAmbient",
        "file": "Sandbox/A1/GL1/KzBridge.lean",
        "sha256": "5eb1114a674dc6f15a63a33e80d4848a93c9c0283343a24e7aa3f808ac662669",
        "also": [
          "HybridQuantumLean.A1.GL1Newton.KzBridge.nuGenSet_subset_KzAmbient",
          "HybridQuantumLean.A1.GL1Newton.KzBridge.clause_iii_Kz",
          "HybridQuantumLean.A1.GL1Newton.KzBridge.clause_i_Kz",
          "HybridQuantumLean.A1.GL1Newton.KzBridge.mem_UevKz_iff_Newton"
        ]
      },
      "literature": [],
      "convention_frame": "As row 01. The Lean bundle is proved over K_1 = Q(v,t), which STRICTLY CONTAINS the K_t = Q(v)[t^{±1}] that goalv0a Definition 1 names — recorded as finding F4, a strengthening. This row is what makes the strengthening harmless rather than a change of statement.",
      "ancestry": "PREDECESSOR LOCATED 2026-08-13, after the acquisition arrived — this row previously read 'none located'. CARD: lit-cahen-chabert-vandermonde-coefficient-descent (Librarian, 2026-08-13, verified at source). CAHEN-CHABERT, Integer-Valued Polynomials, AMS Surveys 48, PROPOSITION I.3.1 with REMARKS I.3.2(i)-(ii), printed p. 9 (section I.3 'Trivial cases', subsection 'Vandermonde' — NOT section I.2 Localization, which is adjacent only). Prop I.3.1: for D a domain in a field L and f of degree n with coefficients in L, if f takes values in D at n+1 points a_0..a_n of D, then d*f is in D[X] where d = prod_{i<j}(a_j - a_i) is the Vandermonde. Remark I.3.2(i) draws exactly this row's claim: 'if E is an infinite subset of K, then a polynomial with coefficients in a LARGER FIELD which maps E into D is in fact a polynomial with coefficients in K. Hence there is no lack of generality in defining Int(E,D) as a subset of K[X].' Remark I.3.2(ii) names the enlarged-ambient object Int(E,D,L) and records that it is a genuinely NEW object only when E is FINITE. Ours is infinite. FRAME: their D is our A_t = Z[v^{±1},t^{±1}] (infinite domain); their K is Frac(A_t) = Q(v,t); their L is any larger field; their E is our multiplicative grid {q^chi : chi in Z}; their Int(E,D) is N^ev. Their hypotheses hold verbatim: the nodes q^chi lie IN the domain, not merely in its fraction field. WHY THE SHARP FORM MATTERS AND THE REMARK ALONE WOULD NOT: Remark I.3.2(i) lands the coefficients in the QUOTIENT FIELD, whereas this row needs them in F_t = Q(v)[t^{±1}], which is NOT a field. Prop I.3.1 is sharper than the remark drawn from it — it lands them in (1/d)*A_t with d an EXPLICIT product of node differences. Since every node is a power of q, that d lies in Z[q^{±1}] and carries NO t, so no t can enter a denominator: the non-field landing is exactly what the explicit Vandermonde gives. ADJACENT AND EXPLICITLY REJECTED (recorded so nobody re-searches them): all of section I.2 (localizes the target domain or the evaluation set, never the ambient); IV.3 Prop IV.3.4 / Cor IV.3.5 pp.82-84 (vary the evaluation SUBRING); section IV.4 (integral closure of Int(E,D), a different question); Ch IV Exercise 3 p.91 (E in F in K with F a subfield — again the evaluation set); and Harman-Hopkins section 4 Prop 4.3, rejected earlier and still rejected. Across the whole book exactly THREE passages vary a field at all, and only p.9 varies the ambient.",
      "warrant": "blue",
      "axioms": [
        "propext",
        "Classical.choice",
        "Quot.sound"
      ],
      "notes": "These five declarations are the ENTIRE contents of the release log the closure signature cites (finding F-E1). Recorded by design and not a gap: clause (ii) has NO separate K_t form, because Definition 3 takes the centre AFTER base change to Frac(A_t) = K_1, so the centre object's ambient is intrinsically K_1. The three-engine faithfulness panel graded that reading FAITHFUL unanimously across both passes. ANCESTRY UPGRADED 2026-08-13 from 'none located' to a located predecessor (Cahen-Chabert Prop I.3.1, p.9) once the acquisition arrived and was read. The failed search that preceded it is retained in ANCESTRY.md §7.3 as the honest record of what was searched before the book was held — a 'none located' that later resolves is not an error, it is the search working.",
      "ancestry_print": "Cahen–Chabert, Prop. I.3.1 with Remarks I.3.2, p. 9 — see Sources."
    },
    {
      "id": "A0a-10-instrument",
      "informal": {
        "statement": "The GL1Newton package computes the object set of goalv0a — the divided classes, the grid, the Newton coordinates, and the three membership predicates — and separates them as the theory requires.",
        "file": "almanac/GL1Newton/README.md",
        "sha256": "8f33751e2b3b38dc8e050e768be6dc5cce37d26f580682f1c4b2c6d40efdbdc6",
        "label": "THE INSTRUMENT (adopted into this edition 2026-08-13; ADOPT confirmed by the record owner)"
      },
      "cas": {
        "object": "the ten GL1Newton stems + the four QFunctions stems",
        "package": "GL1Newton",
        "version": "0.1.0",
        "provenance": "extracted verbatim from HybridQuantum/src/A1/gl1_newton.jl (BQ-13, 2026-07-20) at estate commit 7ddb2e8f, source sha256 2a2fe469…ff2c72; extracted 2026-08-10 with the notation migration applied and four recorded test adaptations. A PINNED SNAPSHOT, not independently developed."
      },
      "lean": null,
      "literature": [],
      "convention_frame": "Current symbols throughout (q, v, t) — the package was migrated on 2026-08-10, unlike the Lean sources and unlike every card. Stems are IDENTIFIERS, not notation: the three-world same-name contract survives the migration by design.",
      "ancestry": "AN INSTRUMENT — this row records a Julia package, and criterion 13 binds results, so ancestry is owed by results alone; owing a predecessor search to an instrument would be a category error (ruled at the form level, 2026-08-13). Recorded in this category shape, replacing the field's previous 'none located' wording — an assertion dressed as a finding — corrected 2026-08-13.",
      "warrant": "orange",
      "declared_range": "Acceptance battery 87/87, re-measured 2026-08-13 (Oscar 1.8.0, Julia 1.12.6). Ranges: grid integrality r ∈ 0..8 × χ ∈ −9..9 (171 cases); triangularity r ∈ 0..8; bridge identity 0 ≤ r ≤ m ≤ 8 (45 pairs); trap-4 separation k ∈ 0..6; frame controls χ ∈ −4..4, r ∈ 0..4; negative control 171 + 78 cases, all required to FAIL and doing so. newton() default verdict window χ ∈ −12..12.",
      "axioms": null,
      "notes": "NOT kernel-certified and cannot be: NO LEAN DECLARATION STATES THE CODE'S BEHAVIOUR. This is the manifest's §9 rule 1 and the record owner's explicit instruction on adoption — adoption makes the package a row, not a certificate. The 87/87 figure is the Editor's own measurement; three records carry '70/70' and a static count of the test file gives 83 (finding F-E4). The edition ships the number it measured and names the discrepancy rather than repeating a figure it could not reproduce.",
      "ancestry_print": "A computation, not a theorem; its warrant is the range above.",
      "evidence_anchor": "almanac/GL1Newton/test/runtests.jl — the battery and its bounds; re-run 2026-08-13 under the heavy-compute gate"
    },
    {
      "id": "A0a-11-n1-referee-pin",
      "informal": {
        "statement": "Clause (iii) is refereed independently of the proof: the evaluation-defined predicate and the span-defined predicate agree, with no disagreements, on positive samples, adversarial seeds and a separator.",
        "file": "n1_clause3_referee_pin.jl",
        "sha256": "6cb7108c675da7f4659e1fe9f55c3a8203a34f86b49407ba4065e1c125cffecb",
        "label": "THE ORACLE GATE for clause (iii) (finding N1 arc, closed 2026-07-21)"
      },
      "cas": {
        "object": "newton vs mem_span, measured non-circularly",
        "package": "HybridQuantum (the development substrate, not the extracted package)",
        "version": "BQ-13 build, 2026-07-21"
      },
      "lean": null,
      "literature": [],
      "convention_frame": "Legacy symbols (Q, q, z) — this pin predates the 2026-08-10 migration and was NOT migrated. Its Q is today's q and its z is today's t.",
      "ancestry": "AN INSTRUMENT — this row records an oracle run, and criterion 13 binds results, so ancestry is owed by results alone; owing a predecessor search to an instrument would be a category error (ruled at the form level, 2026-08-13). Recorded in this category shape, replacing the field's previous 'none located' wording — an assertion dressed as a finding — corrected 2026-08-13.",
      "warrant": "orange",
      "declared_range": "window = 8; 60 random positive samples (x^u ν_r(x), u ∈ 0..5, r ∈ 0..4, coefficients q^{rand(−3..3)} t^{rand(−2..2)}·rand(−5..5)); 5 named adversarial seeds, all required to be REFUTED by both predicates; 1 separator (ν_1, required to be in the lattice and the span but NOT in the Laurent ring); random seed fixed at 20260721. Recorded verdict: PROVED_BOUNDED, disagreements = 0.",
      "axioms": null,
      "notes": "THIS ROW EXISTS BECAUSE OF A REAL DEFECT, and the edition prints the defect rather than only the fix. The substrate's original newton() was defined by ν-span, so it could NOT referee clause (iii) — the claim that the evaluation-defined lattice EQUALS the span — without circularity. The oracle gate was therefore unable to confirm the theorem independently of the proof until the predicate was redefined by evaluation. This is the strongest computational evidence in the edition and it is still a BOUNDED verdict about a Julia program (EMBEDDING_NOTE.md §2c).",
      "ancestry_print": "A computation, not a theorem; its warrant is the range above.",
      "evidence_anchor": "n1_clause3_referee_pin.jl with its recorded verdict in n1_clause3_referee_pin.out"
    },
    {
      "id": "A0a-12-proof-proves-the-signed-statement",
      "informal": {
        "statement": "The stand-alone proof proves the statement that was signed: proofv0a.tex establishes the three clauses of goalv0a.tex — no clause weakened, none strengthened, no convention changed.",
        "file": "proofv0a.tex",
        "sha256": "bbd6f055bd5aff614d1a6575b24949d8fd2b805ebda20e33e5c706f28713bbae",
        "label": "THE CLAIM EVERY OTHER ROW RESTS ON, AND THE ONLY ONE NO MACHINE CAN SETTLE."
      },
      "cas": null,
      "lean": null,
      "literature": [],
      "convention_frame": "Both documents are read in the CURRENT frame (q, v, t; q = v², t = z²). The first referee read the pre-migration text in the legacy frame (Q, q, z); the migration between them was verified mechanically, not by eye, and is recorded in the chain below.",
      "ancestry": "AN EDITORIAL FACT ABOUT THIS EDITION'S OWN DOCUMENTS, not a mathematical result with predecessors — ancestry is owed by results, and owing a predecessor search to a document-comparison claim would be the category error ruled at the form level 2026-08-13 for A0a-11.",
      "warrant": "ink",
      "axioms": null,
      "referee": {
        "why_this_field_exists": "The ink warrant's own definition names what it did not carry: 'a per-row record of WHO refereed THIS claim and when'. This field is that record, and this row is the first to carry it.",
        "independence": "INTERNAL. Both referees are agents of this project working under the Sandbox Rule, adversarially and recused from their own work. NO EXTERNAL PEER REVIEW HAS TAKEN PLACE. The edition says 'Peer review to date: Internal' on its face and that stays true; ink means refereed, never externally refereed.",
        "chain": [
          {
            "stage": "adversarial mathematical referee",
            "date": "2026-07-20",
            "read": "proofv0a.tex as it then stood, pre-notation-migration",
            "report": "REFEREE_REPORT_PROOFv0a.md",
            "report_sha256": "6e31018c647ebfba656e90a011f497eb81fc00c1798af85b6476065f1db0fb0d",
            "verdict": "CONFIRM-WITH-FINDINGS",
            "on_this_claim": "attack (8), byte-faithfulness to goalv0a.tex — FAITHFUL. Definitions, the algebra and its relations, and all three clauses reproduced without change; the four documented traps checked one by one. One non-blocking phrasing point."
          },
          {
            "stage": "notation migration",
            "date": "2026-08-10/11",
            "read": "the whole manuscript",
            "what": "Q→q, q→v, z→t by the Sandbox-wide dictionary. Argument unchanged, symbols renamed. The no-drift property was verified mechanically by the next referee, not asserted here."
          },
          {
            "stage": "human-facing editorial referee",
            "date": "2026-08-12",
            "read": "proofv0a.tex",
            "read_sha256": "c42cbf8fc204bc04773dc308e9dd4c29efb65d64a3ebc1a2eeaacc6feb875cd1",
            "report": "EDITORIAL_REFEREE_REPORT_2026-08-12.md",
            "report_sha256": "e8034b17455cb0af0476a89fcc1f7b7fe7ebd386293c49a90a231d89743d222b",
            "verdict": "PASS-WITH-EDITS — 2 BLOCKING, 15 EDITORIAL, 12 NIT",
            "on_this_claim": "semantic-drift check against the byte-frozen signed anchor: NO DRIFT, verified MECHANICALLY rather than by eye. Refereed for a competent mathematician OUTSIDE this programme reading the PDF with no access to the record.",
            "read_bytes_kept_at": "informal/versions/proofv0a_pre-editorial_2026-08-12.tex"
          },
          {
            "stage": "revision",
            "date": "2026-08-12",
            "what": "Both BLOCKING findings repaired — one-sentence each. The repairs are visible as three hunks against the version above: the migration paragraph restated, the clause (ii) injectivity step written out in full, and the attribution remark made exact. The middle one writes the FIRST referee's own supplied argument into the text."
          },
          {
            "stage": "acceptance",
            "date": "2026-08-13",
            "by": "hypervisorA, as tree owner and review counterparty",
            "document": "EDITION_ACCEPTANCE_2026-08-13.md",
            "document_sha256": "2e9d82647107ae3b1b245ac0bf06e189d0e65c9605a9870674a54f0fe392d899"
          }
        ],
        "the_limit_stated": "NO REFEREE READ THE SHIPPED BYTES. The last referee read c42cbf8f…, required two one-sentence repairs, and those repairs produced the shipped bbd6f055…. THIS IS NOT WITHDRAWN BY THE VERIFICATION BELOW: a delta check by the accepting seat is weaker than a referee reading the whole document, and ink means refereed. The verification sits under this limit as mitigation, never as replacement, and 'Peer review to date: Internal' stands.",
        "delta_verification": {
          "by": "hypervisorA, the accepting seat, 2026-08-31 — who attacked this limit on request rather than ruling it ordinary",
          "reproduced_by": "TWO SEATS, TWO INDEPENDENT IMPLEMENTATIONS, on the stronger form of the test. The Almanac Editor re-ran hypervisorA's environment/label diff before adopting it and extended it to full statement BODIES (6 of 6 identical); hypervisorA then re-implemented the body comparison by a different route and got the same result. Neither seat took the other's number.",
          "what_was_compared": "versions/proofv0a_pre-editorial_2026-08-12.tex (c42cbf8f…, the refereed bytes) against informal/proofv0a.tex (bbd6f055…, the shipped bytes)",
          "size_of_delta": "29 changed lines across three sites",
          "the_decisive_test": "A mechanical diff of every theorem / lemma / proposition / corollary / definition environment and every \\label. EMPTY: six environments in each, identical, same labels. Carried further by the Editor to the full statement BODIES, whitespace-normalised: 6 of 6 identical. NO STATEMENT CHANGED BETWEEN THE REFEREED BYTES AND THE SHIPPED BYTES.",
          "direction_of_the_three_deltas": [
            "the notation-dictionary paragraph expanded — expository, making Q→q, q→v, z→t explicit",
            "the middle-equality step: the refereed text ASSERTED that Uev = Nev ⊆ U maps into U ⊗ Frac(A_t); the shipped text PROVES it — F_t injects into Frac(A_t) = ℚ(v,t) and U is free over F_t, so the inclusion is literal. A justification SUPPLIED where one was assumed.",
            "the Lusztig remark made precise and given the sentence 'Nothing below rests on that remark' — reliance on an external remark REMOVED."
          ],
          "what_it_licenses": "Every delta runs toward more rigour and none touches a statement, so a referee who passed c42cbf8f could not have withdrawn that verdict on bbd6f055: the shipped bytes are strictly better supported than the bytes that earned the PASS. WHAT IT DOES NOT LICENSE: calling the shipped bytes refereed. They are not.",
          "reproduce_it": "diff the two files' \\begin{theorem|lemma|proposition|corollary|definition} and \\label lines; both are kept in informal/versions/."
        }
      },
      "notes": "THIS ROW EXISTS BECAUSE THE EDITION WAS SILENT ON ITS OWN LOAD-BEARING CLAIM. Every other row presupposes that the proof proves the signed statement, and nothing recorded it as a result with a warrant. It cannot be blue: a kernel certifies a formal statement and cannot compare two documents. It cannot be orange: no computation adjudicates whether one text proves another. It is exactly what the ink warrant is for — a written argument, read by an independent adversarial referee — which is also why an edition with zero ink rows was understating its own record rather than reporting it.",
      "ancestry_print": "An editorial fact about this edition's documents; its warrant is the referee chain above.",
      "evidence_anchor": "REFEREE_REPORT_PROOFv0a.md attack (8) and EDITORIAL_REFEREE_REPORT_2026-08-12.md's drift check, with both refereed versions kept in informal/versions/."
    }
  ],
  "row_completeness": {
    "rows_total": 12,
    "rows_dropped": 0,
    "definition": "A field is POPULATED, ABSENT-BY-DESIGN, or MISSING. Absent-by-design requires a declaration below: a class-level reason and the rows it covers, by full id. MISSING is non-populated and covered by no declaration, and refuses the build. A CITED FILE WITHOUT ITS HASH CAN NEVER BE DECLARED ABSENT BY DESIGN: the hash of a file that exists is always measurable, so its absence is always a defect.",
    "rows_fully_populated": 5,
    "rows_with_declared_design_absences": 7,
    "rows_with_missing_fields": 0,
    "invariant": "rows_fully_populated + rows_with_declared_design_absences + rows_with_missing_fields = rows_total - rows_dropped",
    "figures_are_derived": "Every number here is counted from the rows by derive_completeness.py and none is typed. The figures this replaces were derived from the NUMBER OF ENTRIES in a list while their names said rows: 9 fully filled where the count is 5, and 2 rows with a named missing field where four rows were named across two entries.",
    "which_rows_are_fully_populated": [
      "A0a-01-clause-i",
      "A0a-03-clause-iii",
      "A0a-04-lemma-grid",
      "A0a-05-lemma-fwd",
      "A0a-06-lemma-rev"
    ],
    "design_absence_declarations": [
      {
        "class": "no manuscript environment",
        "reason": "A formal-side guarantee with no counterpart passage in the manuscript. The row is kept with the field named rather than dropped, and rather than inventing a manuscript environment to fill a column.",
        "fields": [
          "informal.file",
          "informal.sha256"
        ],
        "rows": [
          "A0a-08-nondegeneracy",
          "A0a-09-kz-bridge"
        ]
      },
      {
        "class": "no computational claim",
        "reason": "The content is definitional, or the claim is not one a computation can adjudicate. The edition does not manufacture a CAS object to fill a column.",
        "fields": [
          "cas.object",
          "cas.package",
          "cas.version"
        ],
        "rows": [
          "A0a-02-clause-ii",
          "A0a-07-definition-1-presented",
          "A0a-09-kz-bridge"
        ]
      },
      {
        "class": "no Lean counterpart",
        "reason": "The row is about the instrument or the oracle gate itself, not about a statement a kernel could certify. There is no declaration to name and therefore no axiom set to measure — a fact about the result, not a gap in the record.",
        "fields": [
          "lean",
          "axioms"
        ],
        "rows": [
          "A0a-10-instrument",
          "A0a-11-n1-referee-pin"
        ]
      },
      {
        "class": "no literature leg",
        "reason": "No predecessor is cited for this row: either none was located and the search is recorded in ANCESTRY.md, or the row is about this edition's own apparatus rather than about a result with ancestry.",
        "fields": [
          "literature"
        ],
        "rows": [
          "A0a-07-definition-1-presented",
          "A0a-08-nondegeneracy",
          "A0a-09-kz-bridge",
          "A0a-10-instrument",
          "A0a-11-n1-referee-pin"
        ]
      },
      {
        "class": "not a claim a machine can state",
        "reason": "The row's claim is that one human-readable document proves what another one signs. A proof kernel certifies a formal statement and cannot compare two documents; no computation adjudicates whether one text proves another; and the claim is about this edition's own manuscripts, so it has no predecessor in the literature. THESE ABSENCES ARE THE MEANING OF THE INK WARRANT, NOT GAPS BESIDE IT — recording them as gaps would invert the row. What the row DOES carry, and no other row does, is a per-row referee record: who read it, when, at which hash, with what verdict.",
        "fields": [
          "cas",
          "lean",
          "axioms",
          "literature"
        ],
        "rows": [
          "A0a-12-proof-proves-the-signed-statement"
        ]
      }
    ],
    "the_honest_headline": "All 11 rows are accounted for: 5 have every field populated, 6 carry an absence that is declared with its reason and its full row ids, and 0 have a field that is neither. An absence recorded with its reason is a fact about the result; an absence nobody named would be a defect, and the build now refuses one."
  },
  "ancestry_note": "Every row carries an ancestry field, and every 'none located' has a recorded search behind it (query, shelf, date) per manifest §6. Instrument rows declare their category explicitly. Edition-level searches run 2026-08-13; the manuscript-level criterion-13 cycle is informal/CITATION_VERIFICATION_2026-08-09.md. CARDS TRAVEL: every cited source now resolves to a card on the shelf — the two newest, lit-gramain-geometric-progression-integer-valued-basis and lit-cahen-chabert-vandermonde-coefficient-descent, were written by the Librarian on 2026-08-13 and read at source.",
  "accepted": "ACCEPTED by hypervisorA as tree owner and review counterparty, 2026-08-13 — typed record at sandboxA0a/informal/EDITION_ACCEPTANCE_2026-08-13.md, on REQUEST 20260813T145357Z-editor-96569-9a6a. Acceptance means the edition is a faithful and non-overclaiming account of the closed record; deposit, outward release and the row-freeze are separate later acts.",
  "evidence_anchor_note": "Manifest §11.2: a row records the RANGE of its computation and an ANCHOR to the certificate, and NEVER prints the computed values. A reader wanting the values follows the anchor. The moment a row prints its samples it has stopped being a warrant and become the forbidden thing."
}