[jacobalansussman]

Change and mathematical scope

Adds one package, research/eth-claim-fft-impact: a map of what OpenAI's reported disproof of the Exponential Time
Hypothesis (preprint of 26 October 2026, under examination by a working group led by Russell Impagliazzo,
Ramamohan Paturi and Ryan Williams) would change for multiplication, the DFT and the WHT, if the claim holds.
It is an audit of conditional results, not a construction or a proof. No new κ; no record, target or frozen
package changes.

Finding, if the claim holds	Status
No selected or historical κ record moves; I found no κ record, target, certificate or framework assumption on the hub that uses ETH, SETH or the Orthogonal Vectors Conjecture (OVC)	argued by hand; search limits in README Sources
ETH, SETH, Gap-ETH, NSETH, #ETH and their randomized versions fall, plus some lower bounds outside the FFT world that the algorithm beats directly (e.g. "no 2^(o(v))" for colouring; Curticapean's perfect-matching bound)	follows if the claim holds
Every theorem stands: the unconditional lower bounds, the non-rigidity and fast-transform results, my Lean-checked savings (1.7887045e-3 DFT, 1.5699306e-3 WHT)	theorem
Afshani–Freksen–Kamma–Larsen's Ω(n log n) rests on the Li–Li network-coding conjecture, not on ETH	conditional on Li–Li; unaffected by this claim
Alman–Li's "no near-linear depth-2 WHT circuit" loses its SETH leg and stands on OVC alone (their proof needs only that #OV in dimension O(log N) is not in N^(1+o(1))); OVC is not refuted by any known reduction but loses its usual derivation from SETH	conditional on OVC; argued by hand
SETH-based Subset Sum (Abboud–Bringmann–Hermelin–Shabtay), ETH-based k-SUM (Pătraşcu–Williams) and the NSETH barrier lose their basis without being refuted	follows if the claim holds; partly recalled
Williams 2013 Thm 6.1 fires (E^NP ⊄ SIZE(O(n))), plus the preprint's c·n·√(log n) corollary for one E^NP language, which needs the appendix-only sparse bound; nothing aimed at transforms, no rigid matrix, no linear-circuit bound	follows if the claim holds; argued by hand
No practical speed-up: with constants set to 1 the exponent factor is 0.73 at n = 10^4; the sharper exponent beats 1.307^n only beyond about n = 10^79	computed (verify.py)
Speculation: whether the preprint's interpolation parameters improve the polynomial behind Alman–Williams / Alman–Guan–Padaki rigidity upper bounds; whether its tensor-contraction theorem can count orthogonal vectors after a low-degree split (the direct encoding breaks its degree cap)	speculation

Remaining obligations: the claim itself (the working group's examination); the results marked "recalled" in the
README were not re-read; the hub search used a local copy from 22 October plus GitHub search, which can miss files;
no person has reviewed the map (one AI reviewer attacked every step).

Task and overlap

• Base de5ec2e7a6074068452f45b1a191b5c72832df4a, priority revision 8. Card scope-navigation (method "Index one
  tightly related family of obstructions with explicit excluded and open hypotheses"), scope_status: refined:
  the family is the conditional results touching the ETH family, and every entry is conditional on an outside claim
  under review. Reason in TASK.json.
• No live inputs. Provenance rows: the task catalogue and certificates/selected-result.json (κ = 62009/20000000).
• Nearest work: Construct Gaussian spectral and precision compilers from the ETH preprint #5813 and Construct exact Gaussian corrections with pruned and mixed precision circuits #5815 (Dugongue) carry the preprint's techniques to the Gaussian axis and claim no κ; this
  package adds the map of which conditional results move, and links them instead of repeating them. Research notes (no κ claim): #109 and lower bounds, the coding gap, a Lorentzian minrank obstruction, and a loss chain #634
  (ShikeChen01) and discussion FINDING: κ and undirected coding gaps (oblivious padded multiplier, AFKL with a gap, BH/BGS exponent) #2838 (philippeVV) cover the network-coding side; this package only cross-references
  them. I found no hub package or discussion that maps ETH, SETH or OVC; that is a search result, not a proof of
  novelty.

Validation

python3 scripts/research_package.py --package research/eth-claim-fft-impact --check-only
python3.12 -B scripts/research_package.py --package research/eth-claim-fft-impact
# = python3 -B research/eth-claim-fft-impact/verify.py   (PASS_ETH_CLAIM_FFT_IMPACT)
python3 -B scripts/check_research_commit.py --package research/eth-claim-fft-impact

Standard library only. verify.py passes with Python 3.12.13 and 3.9.6 on an Apple M4 (macOS) in about 0.03 s and
19 MB, and leaves no files behind. It recomputes the five figures of README section 5 (0.7316, 0.7064 and 0.5096
for the exponent factor at n = 10^4, 10^6 and 10^30; 10^78.7 and 10^2390.2 for the two thresholds), checks that the
README prints each one, and rejects four false figures as failure controls. Everything else is a reading of sources
or an argument by hand, labelled as such. Not run: the card's first step (scripts/research_selected_baseline.py),
the preprint's Lean build, and any check of the preprint's proofs.

Credit

OpenAI for the preprint (no individual authors named) and the working group led by Impagliazzo, Paturi and
Williams for the examination. Josh Alman and Baitian Li; Afshani, Freksen, Kamma and Larsen; Ryan Williams; Jahanjou,
Miles and Viola; Alman and Williams; Dvir and Liu; Alman, Guan and Padaki; Alman and Rao; Alman and Chen; Zongpeng Li
and Baochun Li; and the other authors credited where their results are used in the README. Dugongue (#5813, #5815),
ShikeChen01 (#634) and philippeVV (#2838) on the hub.

Substantial AI assistance: the map, the check and the text were written by AI agents (Anthropic Claude) under my
direction. No independent human review is claimed. Apache-2.0.

Open next questions

In README (## Open next questions) and TASK.json. The smallest useful follow-ups: compare the preprint's
interpolating polynomial with Alman–Williams's at equal degree (share of entries each gets wrong); test one gadget
that splits the vector tables of an Orthogonal Vectors instance across low-degree vertices, so the preprint's
tensor-contraction theorem applies; re-read the map when the working group reports.

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