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Search the paper sections, open their original context and follow the checks they actually cite. The knowledge atlas explains the result; this library locates its source.

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403 sections found. Current publication documents are listed before historical material.

2026-07-21 (XV) ( v505 — WP5e- [formula in source] of CELEST.SEAM.01 ``the equivariant anomaly ledger on twistor space'' promoted as CELEST.WP5E.BETA.01: the Atiyah–Bott/Lefschetz fixed-point skeleton of the one-loop twistor inflow is EXACT — denominators [formula in source] with Dedekind sum [formula in source] , equivariant characters [formula in source] by two routes, invariant Okubo [formula in source] with the twisted sectors NOT reducing and the AB sum leaving the RIGID residual [formula in source] , the index bridge [formula in source] exact with glue defect [formula in source] both routes, the level dials [formula in source] geometric (current count [formula in source] ), and the honest E3 REFUTATION: [formula in source] fills the GRAVITON slot [formula in source] , NOT the axion slot [formula in source] — the three sphere classes fill the three twisted axion slots instead; the preregistered kill (``inflow demands a level [formula in source] '') does NOT fire on the equivariant skeleton; WP5e: [formula in source] (CFT side, v502) [formula in source] [formula in source] (equivariant twistor skeleton, v505) executed, the global BCOV quantisation stays ; Wolfram extension [formula in source] (verified engine run); SEAM.EQUIV.01 stays , no marker moves)

Research changelog · TFPT — Introduction and reading guide

v505_celestial_wp5e_beta_equivariant_ledger.py ( CELEST.WP5E.BETA.01, 47 checks, [formula in source] 1.3 s; sympy/Fraction exact, no floats; deterministic). The twistor side of WP5e pushed as far as exact arithmetic reaches: the Atiyah–Bott/Lefschetz skeleton of the one-loop box anomaly (Costello; Bittleston–Sharma–Skinner) on [formula in source] with the [formula in source] [formula in source] -glue monodromy. AB le

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Source location and explicit evidence links

documents/changelog/sections/006-source.tex · lines 123 to 173

These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.

2026-07-21 (XIV) ( v504 — WP5d- [formula in source] of CELEST.SEAM.01 ``split [formula in source] strong additivity from the lattice'' promoted as CELEST.WP5DB.01: the two remaining KLM legs of complete rationality witnessed for the orbifold prescription — strong additivity ALGEBRAICALLY EXACT with the shared boundary Majorana ( [formula in source] , GF2 spans full, rank [formula in source] ; disjoint exactly index [formula in source] [formula in source] the v501 [formula in source] bit), the entropic touching defect BOUNDED [formula in source] with the Ising [formula in source] -exponent approach ( [formula in source] ) while the preregistered [formula in source] /Dirac control DIVERGES (Klich–Levitov pinned, infinite index), the split property at the elliptic-nome rate [formula in source] ( [formula in source] – [formula in source] ) with EXACT orbifold inheritance ( [formula in source] [formula in source] the [formula in source] compound — Longo heredity), and Pimsner–Popa [formula in source] identically ( [formula in source] , [formula in source] , [formula in source] — two independent index routes); with v501 ALL THREE KLM ingredients carry lattice witnesses; the continuum uplift stays \ — ``finite-group orbifolds of completely rational nets are completely rational'' is XU'S THEOREM, cited not claimed; Wolfram extension [formula in source] (verified engine run); SEAM.EQUIV.01 stays , CELEST.SEAM.01 stays Open, no marker moves)

Research changelog · TFPT — Introduction and reading guide

v504_celestial_wp5d_klm_completeness.py ( CELEST.WP5DB.01, 37 checks, [formula in source] 12 s; numpy/scipy Gaussian machinery ED-validated [formula in source] exact GF2/integer algebra; deterministic). Complete rationality (Kawahigashi–Longo–M\"uger) [formula in source] split [formula in source] strong additivity [formula in source] finite two-interval [formula in source] -index; v501 (WP5d- [formula in source] ) wi

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documents/changelog/sections/006-source.tex · lines 174 to 231

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2026-07-21 (XIII) ( v503 — the v215 deferred emergence test (lever 7) executed light and promoted as QGEO.EMERGE.LIGHT.01: NO dynamical selection of the square modulus — the free field's global [formula in source] winner is the hexagonal torus, [formula in source] is a saddle, criticality at the square is Palais symmetry; the square is pinned by rigidity alone (the raw DtN is mod- [formula in source] block-diagonal iff [formula in source] , an isolated zero); and the residual converges: QGEO-R1 [formula in source] P2-R1 [formula in source] one common rest, ``why does the raw seam carry the order- [formula in source] clock''; Wolfram extension [formula in source] (verified engine run); NO marker moves — QGEO.REALIZE.01 stays / , AX.P2.01 stays a declared axiom)

Research changelog · TFPT — Introduction and reading guide

v503_qgeo_emergence_light.py ( QGEO.EMERGE.LIGHT.01, 17 checks; mpmath [formula in source] digits [formula in source] v280-style lattice DtN [formula in source] sympy exact). The v215 lever 7 (``the decisive kill is deferred: compute the raw seam-collar DtN without inputting the marks and check whether four square marks emerge'') executed in its first honest light version. No dynamical selection: [formula in source]

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documents/changelog/sections/006-source.tex · lines 232 to 279

These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.

2026-07-21 (XII) ( v502 — WP5e- [formula in source] of CELEST.SEAM.01 ``prefactor and level bookkeeping'' promoted as CELEST.WP5E.ALPHA.01: the [formula in source] prefactor of [formula in source] IS exact [formula in source] vacuum-energy bookkeeping (the clock is inner [formula in source] shift orbifold [formula in source] , common [formula in source] ; discriminant form [formula in source] Casimir via spectral flow AND [formula in source] -Majorana free fermions), and [formula in source] is forced THREE independent ways (current condition; conformal embedding; central charge [formula in source] the prefactor itself; plus the WP5b singular-vector dial [formula in source] ); honest sharpening: glue- [formula in source] integrality holds for ALL [formula in source] and fixes nothing; the BCOV/Costello–Li twistor inflow stays \ — WP5e is subdivided ( [formula in source] done, WP5e proper open); Wolfram extension [formula in source] (verified engine run); SEAM.EQUIV.01 stays , no marker moves)

Research changelog · TFPT — Introduction and reading guide

v502_celestial_wp5e_prefactor_level.py ( CELEST.WP5E.ALPHA.01, 33 checks, exact sympy/Fraction, no floats). The two exactly computable consistency anchors of the WP5e twistor uplift established. Part A — the prefactor: Hurwitz- [formula in source] exact ( [formula in source] ; [formula in source] ; Ising shift [formula in source] per Majorana); the clock is inner ( [formula in source] and [formula in source] both rea

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documents/changelog/sections/006-source.tex · lines 280 to 330

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2026-07-21 (XI) ( v501 — WP5d- [formula in source] of CELEST.SEAM.01 ``the two-interval index from the lattice'' promoted as CELEST.WP5D.01: the KLM Haag-duality discriminator measured entropically on the seam edge — the [formula in source] -layer carrier saturates the [formula in source] offset at machine precision, [formula in source] the v490 census, and the condensation arithmetic [formula in source] closes with [formula in source] ; the preregistered KILL (`` [formula in source] -offset [formula in source] after condensation'') does NOT fire; contract now ``WP1–WP5d executed; WP5e the single remaining milestone''; Wolfram extension [formula in source] (verified engine run); SEAM.EQUIV.01 stays , no marker moves)

Research changelog · TFPT — Introduction and reading guide

v501_celestial_wp5d_two_interval_index.py ( CELEST.WP5D.01, 39 checks, numpy/scipy Gaussian machinery [formula in source] exact Fractions). The WP5d roadmap discriminator — [formula in source] (Haag-dual two-interval net, one sector) vs [formula in source] — executed at the [formula in source] (lattice-index) stage on the v367 seam edge ( [formula in source] critical Majorana layers, [formula in source] , v450-style

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documents/changelog/sections/006-source.tex · lines 331 to 374

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2026-07-21 (X) ( v500 — WP5c of CELEST.SEAM.01 ``the GNS limit state'' promoted as CELEST.WP5C.01: the quasi-free family [formula in source] exists, is positive, stabilises exactly at the WP5a threshold, and its limit carries the null ideal in its GNS kernel — the full [formula in source] -block exact level-2 Gram has rank [formula in source] exactly with kernel [formula in source] weight by weight; [formula in source] IS the GNS zero vector (the WP5b S4.10 tension resolved at the state level); a CCR obstruction proves the family formulation necessary; preregistered SUCCESS criterion met, KILL not triggered; Wolfram extension [formula in source] (verified engine run); SEAM.EQUIV.01 stays , no marker moves)

Research changelog · TFPT — Introduction and reading guide

v500_celestial_wp5c_gns_limit_state.py ( CELEST.WP5C.01, 35 checks, exact integer/Fraction, no floats, deterministic). WP5a ( v497) made the boundary limit precise, WP5b ( v498) built the deleting operator; WP5c constructs the state. [formula in source] is quasi-free: loop sector [formula in source] the affine [formula in source] vacuum [formula in source] -point functions via the machine-determined compact anti-invo

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documents/changelog/sections/007-source.tex · lines 1 to 46

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2026-07-21 (IX) ( v499 — the P2 weight-typing postulate HARDENED: the anchor [formula in source] typed as the Birkhoff–Grothendieck splitting exponents of the Deligne canonical extension, so integrality/positivity/sum- [formula in source] become theorems given the \ anchors; the v491 check-9 residual sharpened, the tfpt_2 ``balanced'' selection typed as stability; Wolfram extension [formula in source] (verified engine run); no gate closes, no marker moves — AX.P2.01 stays a declared axiom, QGEO.SYM stays )

Research changelog · TFPT — Introduction and reading guide

v499_p2_weights_deligne_bg.py ( P2.TYPING.01, 23 checks, sympy exact, no floats). v491 reduced P2 to `` [formula in source] positive integers summing to [formula in source] ''; its residual was the typing (why integers, why positive, why sum [formula in source] ). Now typed: given the \ anchors ( [formula in source] marks, v216; rank [formula in source] , v137/ v228; cusp-class local monodromy [formula in source] and

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documents/changelog/sections/007-source.tex · lines 47 to 94

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2026-07-21 (VIII) (Editorial: dedicated celestial-route section in Paper 3 [formula in source] website mirror — the scattered celestial sentences consolidated into one coherent six-step section; no new scripts, no status changes, no marker moves, SEAM.EQUIV.01 untouched)

Research changelog · TFPT — Introduction and reading guide

tfpt_3_e8_audit_bootstrap: new section ``The celestial route: from the [formula in source] clock to the [formula in source] boundary shadow''. The celestial-contract material that had accumulated as one long paragraph inside ``The M\"obius origin of the irreducible [formula in source] '' is consolidated into a dedicated section (placed after the bootstrap audit, before ``Honest status''), telling the executed WP1–WP5

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documents/changelog/sections/007-source.tex · lines 95 to 125

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2026-07-21 (VII) (CELEST.SEAM.01 WP5b executed and promoted: v498 — ``the singular vector as an operator'', the deleting object of the v497 null ideal constructed explicitly and machine-verified singular; contract now WP1–WP4 [formula in source] WP5a [formula in source] WP5b done, WP5c–e \ (roadmap); Wolfram extension [formula in source] (verified engine run); no gate closes, no marker moves, SEAM.EQUIV.01 untouched)

Research changelog · TFPT — Introduction and reading guide

v498_celestial_wp5b_singular_vector.py ( CELEST.WP5B.01, 53 checks, exact integer/Fraction, deterministic, no floats). Success on the preregistered WP5b criterion: the deleting object exists and is explicit. Construction: [formula in source] (weight [formula in source] , level [formula in source] quarter units [formula in source] , an integer level) in a machine-built Chevalley/Frenkel–Kac basis — bimultiplicative [f

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documents/changelog/sections/007-source.tex · lines 126 to 176

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2026-07-21 (VI) (CELEST.SEAM.01 WP5a executed and promoted: v497 — ``the null ideal from the limit'', the v496 boundary-limit shadow made a precise coefficientwise limit and the level-2 null ideal derived from root data; contract WP5 subdivided, now WP1–WP4 [formula in source] WP5a done, WP5b–e \ (roadmap); Wolfram extension [formula in source] (verified engine run); no gate closes, no marker moves, SEAM.EQUIV.01 untouched)

Research changelog · TFPT — Introduction and reading guide

v497_celestial_wp5a_null_ideal.py ( CELEST.WP5A.01, 34 checks, exact integer/Fraction, no floats). Three results make the WP4 limit reading precise. Stabilisation theorem: the one-parameter family [formula in source] of graded Fock characters on the chiral jet generators (loop energy [formula in source] , radial number [formula in source] ; [formula in source] in quarter units [formula in source] ) contains the chira

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documents/changelog/sections/007-source.tex · lines 177 to 221

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2026-07-21 (V) ( comb-meta-limit re-run with the PG.06b FULL Vela recovery ingested — the stale single-obs PG.06b reference (noise-peak [formula in source] \,Hz) corrected in the channel definitions; the new X-ray channel enters censored (no absolute [formula in source] ), both aggregate limits numerically unchanged; experiments level only — no verification module, no gate closes, no marker moves)

Research changelog · TFPT — Introduction and reading guide

experiments/comb-meta-limit channel update (methodology untouched). The Vela X-ray channel ( channels.py) now ingests the PG.06b FULL reduction ( pg06b_full_vela.json in pulsar-glitch-recovery/results: 665 obs [formula in source] 491 usable [formula in source] 119 segment-coherent [formula in source] points) instead of the superseded single-obs pg06b_vela.json; the stale code note quoting the noise-peak ``detection''

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documents/changelog/sections/007-source.tex · lines 222 to 250

These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.

2026-07-21 (IV) (Wolfram engine reactivated — the deferred second-path mirrors VERIFIED: base [formula in source] [formula in source] extension [formula in source] ( [formula in source] , the 16 mirrors accumulated since 2026-07-14 now counted); GATE.WOLFRAM.01/02 and all counter surfaces synced; no gate closes, no marker moves)

Research changelog · TFPT — Introduction and reading guide

Verified engine run 2026-07-21 (Wolfram Engine 14.3, license reactivated). wolframscript -file verification/wolfram/tfpt_readouts.wl [formula in source] 116 passed, 0 failed, ALL WOLFRAM CHECKS PASSED; tfpt_readouts_extension.wl [formula in source] 394 passed, 0 failed, ALL WOLFRAM EXTENSION CHECKS PASSED. The 16 exact mirrors added while the engine was unactivated all enter the counted total ( [formula in source] ):

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documents/changelog/sections/007-source.tex · lines 251 to 268

These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.

2026-07-21 (III) (CELEST.SEAM.01 WP3 [formula in source] WP4 executed and promoted: v495 Green–Schwarz alignment (verdict B, honestly non-selective) [formula in source] v496 character-vs-S-algebra type mismatch (verdict B(ii), boundary-limit shadow); contract now WP1–WP4 done, WP5 ; no gate closes, no marker moves, SEAM.EQUIV.01 untouched)

Research changelog · TFPT — Introduction and reading guide

v495_celestial_wp3_gs_alignment.py ( CELEST.WP3.01, 25 checks, exact Fraction/sympy). The pre-registered WP3 ``alignment test only'': the Okubo coefficient [formula in source] is derived as an exact polynomial identity for all 8 algebras on Costello's list (sl [formula in source] , sl [formula in source] , g [formula in source] , so [formula in source] , f [formula in source] , e [formula in source] , e [formula in s

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documents/changelog/sections/007-source.tex · lines 269 to 309

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2026-07-21 (II) (PG.06b FULL: the complete NICER Vela archive reduced — the first X-ray [formula in source] leg of the recovery-comb search, verdict data_limited; the old PG.06b ``pipeline proven'' fold corrected on record; experiments level only — no verification module, no gate closes, no marker moves)

Research changelog · TFPT — Introduction and reading guide

experiments/pulsar-glitch-recovery PG.06b FULL executed ( tfpt-pulsar vela-full). The full NICER Vela-pulsar (PSR B0833-45) L2 archive is reduced, with the manifest frozen before the bulk download ( manifest_full_reduction.json: all 665 ObsIDs, preregistered 2019/2021/2024 glitch windows, 20-GB abort gate): 665/665 obs downloaded (2.6\,GB, raw gitignored) [formula in source] 491 usable [formula in source] 240 per-obs

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documents/changelog/sections/007-source.tex · lines 310 to 342

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2026-07-21 (the two 2026-07-20 prediction-of-record rows promoted to the suite: v494 — [formula in source] running [formula in source] [formula in source] -distortion branch discriminator machine-checked, ledger rows COSMO.RUNNING.01/ COSMO.MUDIST.01, prediction surfaces synced; no gate closes, no marker moves)

Research changelog · TFPT — Introduction and reading guide

v494_cosmo_running_mu_record.py (23 checks, all green). The [formula in source] -running and [formula in source] -distortion scorecard rows of 2026-07-20 (IV) get their load-bearing module so the new paper/website statements are machine-backed. \ leading-order identities (sympy exact): [formula in source] , [formula in source] (NOT [formula in source] ); LO band [formula in source] : [formula in source] . \ exact slo

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documents/changelog/sections/007-source.tex · lines 343 to 378

These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.

2026-07-20 (VIII) (E8 mass-ladder blind-recovery bed EXECUTED: verdict validated at the detector level — the Cartan–PF ladder pipeline blindly recovers the published Zamolodchikov-E8 spectra of BaCo [formula in source] V [formula in source] O [formula in source] (8/8) and CoNb [formula in source] O [formula in source] (6/8 in-window) and rejects every control class; experiments level only — confirms Zamolodchikov E8, not TFPT; no verification module, no gate closes, no marker moves)

Research changelog · TFPT — Introduction and reading guide

experiments/e8-ladder-bed/ executed (preregistered hypotheses/e8_ladder_bed_v1.yaml). The blind ladder detector (assignment DP [formula in source] scale fit [formula in source] 5000-ladder Monte-Carlo null; the same detector class TFPT uses on search surfaces, e.g.\ hfqpo-ladder) on the only public known-answer mass-ladder dataset: BaCo [formula in source] V [formula in source] O [formula in source] (Zou [formula in

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documents/changelog/sections/008-source.tex · lines 1 to 30

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  • explicit script identifier v1_e8_glue.py

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  • explicit file citation next.txt

    literal source filename/path in TeX

  • cross reference join tfpt_readouts.wl

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  • explicit file citation README.md

    literal source filename/path in TeX

  • cross reference join tfpt_readouts_extension.wl

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2026-07-20 (VII) ( v493 — WP2 of CELEST.SEAM.01 executed: the clock-invariant deformation [formula in source] is a PURE SCALE with the [formula in source] pillowcase frozen, the [formula in source] clock IS the Picard–Lefschetz/Coxeter monodromy of the seam deformation, and the BHS deformed-algebra pattern transfers [formula in source] with no sector leak; verdict B, contract updated to WP2 done, no gate closes, no marker moves, SEAM.EQUIV.01 and the v216 residual stay )

Research changelog · TFPT — Introduction and reading guide

v493_celestial_wp2_clock_deformation.py ( CELEST.WP2.01). WP2 of the celestial contract, sympy exact (47 checks), promoted from the experiments/tfpt-discovery/ probe celestial_seam_wp2_clock_deformation_probe.py. Geometry: [formula in source] forces [formula in source] sharply and two-sided ( [formula in source] ); [formula in source] is smooth iff [formula in source] ( [formula in source] ); the branch points [formu

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documents/changelog/sections/008-source.tex · lines 31 to 72

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2026-07-20 (VI) (HFQPO ``third tooth'': the preregistered archival RXTE PCA scan has RUN — a well-powered null with limits; scorecard row S1.e data_limited [formula in source] null, no marker moves)

Research changelog · TFPT — Introduction and reading guide

H3 stage 2 executed ( experiments/hfqpo-ladder/results/archival/). The preregistered archival scan ( hypotheses/hfqpo_v1.yaml, archival_design) ran end-to-end on public HEASARC data: 77 ObsIDs / 4.42\,GB across all four [formula in source] -pair sources (GRO J1655 [formula in source] 40, XTE J1550 [formula in source] 564, GRS 1915 [formula in source] 105, H1743 [formula in source] 322). Sanity gate PASS (11/12 publis

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documents/changelog/sections/008-source.tex · lines 73 to 97

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  • explicit file citation next.txt

    literal source filename/path in TeX

  • explicit file citation README.md

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  • explicit file citation predictions.txt

    literal source filename/path in TeX

2026-07-20 (V) ( v492 [formula in source] the new research contract CELEST.SEAM.01 — the celestial-holographic route: the [formula in source] [formula in source] -glue is the flat [formula in source] monodromy of the equivariant celestial chiral algebra on the [formula in source] ALE space, with the exact correction clock [formula in source] deck (spin bridge [formula in source] , [formula in source] ); verdict B, no gate closes, no marker moves, SEAM.EQUIV.01 stays )

Research changelog · TFPT — Introduction and reading guide

v492_celestial_z4_orbifold.py ( CELEST.WP1.01). WP1 of the new contract, sympy exact (36 checks): the v128 [formula in source] -glue grading of [formula in source] ( [formula in source] , additive on all [formula in source] root pairs) is inner — [formula in source] reads the glue class mod [formula in source] on all [formula in source] roots, so the glue is [formula in source] , an order- [formula in source] inner t

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documents/changelog/sections/008-source.tex · lines 98 to 130

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  • cross reference join GlueUniqueness.lean

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  • explicit claim identifier status_ledger.csv

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  • explicit script identifier v492_celestial_z4_orbifold.py

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  • explicit claim identifier status_ledger.csv

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  • explicit script identifier v92_glue_uniqueness.py

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  • explicit script identifier v128_graded_hull.py

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  • explicit script identifier v377_seam_s3_e8character.py

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  • cross reference join MobiusUniformisation.lean

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  • explicit claim identifier status_ledger.csv

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  • explicit script identifier v168_qgeo_rigidity.py

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  • explicit script identifier v125_glue_qsystem.py

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  • explicit file citation v492_celestial_z4_orbifold.py

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  • cross reference join AxiomCheck.lean

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  • explicit script identifier v214_seam_pillowcase.py

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2026-07-20 (IV) (evidence scorecard: five new typed rows — the [formula in source] running prediction of record, the [formula in source] -distortion [formula in source] branch discriminator, and three parked analog beds (bosonic-E8 thermal Hall, E8 mass-ladder recovery, Efimov DSI tuning); experiments level only — no verification module, no gate closes, no marker moves)

Research changelog · TFPT — Introduction and reading guide

[formula in source] running (prediction of record, consistent). The Starobinsky branch fixes the running of the spectral index: [formula in source] at [formula in source] (exact slow roll [formula in source] ; band [formula in source] : [formula in source] ) and [formula in source] (leading order; NOT [formula in source] ) — the identity [formula in source] holds only at leading order ( [formula in source] 7\% off ex

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documents/changelog/sections/008-source.tex · lines 131 to 182

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