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Additive combinatorics: Sidon sets and N(h,k) bounds

constellation seal · derived from vfr_496956067dc5ad79
id
vfr_496956067dc5ad79
license
CC-BY-4.0
findings
22
accepted core
1
contested
1
links
0
sources
22
evidence
22
avg conf
0.83

used by 1 · replayed by 1 producer · second seat open

e33/33 · finding.asserted · reviewer:will · 2026-06-03 · null→e123

Reviewable change

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add a finding

verified — A frozen deterministic verifier re-checked the claim and passed.accepted

The polynomial method bounds 3-AP-free subsets of (Z/4Z)^n by 4^{0.926n}, far below the 4^n total, breaking the previous logarithmic-style bounds for cap-set-style problems.

id
vpr_a3f3e64fc4888fc0
frontier
Additive combinatorics: Sidon sets and N(h,k) bounds
kind
finding.add
created
2026-05-09
findings
+1
state
null → f2b2072d

accept gate

1 of 4 on record
—
signature
agent:research-bot-2026-05-09 · no key registered on this bundle
✓
chain
null → f2b2072d
—
witness
no verifier attachment on record for this target
—
grade
in state · unreviewed

timeline

  1. 2026-05-09proposeproposed · finding.addagent — machine actor, no signing keyagent:research-bot-2026-05-09vpr_a3f3e64fc4888fc0Manual finding added to frontier state
  2. 2026-05-09acceptfinding.assertedagent — machine actor, no signing keyagent:research-bot-2026-05-09null→f2b2072dvev_5e54fbcfde90e54fManual finding added to frontier state

proposed

reason

Manual finding added to frontier state

finding type

theoretical

proposed confidence

0.85

confidence basis

operator-supplied frontier prior; review required

provenance

proposed by

agent — machine actor, no signing keyagent:research-bot-2026-05-09

actor type

human

created at

2026-05-09

target type

finding

affected

inspect finding →

The polynomial method bounds 3-AP-free subsets of (Z/4Z)^n by 4^{0.926n}, far below the 4^n total, breaking the previous logarithmic-style bounds for cap-set-style problems.

vf_7273c1823848f6e3

Diff

Read-only frontier; diff not recomputed.

Review chain

  1. 01request

    Change request

    Additive combinatorics: Sidon sets and N(h,k) bounds receives a reviewable source, finding, caveat, replication, evaluation, or proof-affecting edit.

    open review →
  2. 02packet

    Diff packet

    The packet names affected record objects, evidence, rationale, reviewer-facing fields, and expected proof impact.

    open the campaign →
  3. 03checks

    Check output

    Schema, provenance, benchmark, contradiction, and proof checks decide whether the request is ready to read.

    inspect checks →
  4. 04review

    Reviewer decision

    A steward accepts, rejects, caveats, revises, or retracts the request under an inspectable identity.

    read queue →
  5. 05accepted

    Accepted event

    Only the accepted event mutates frontier state. Atlases, constellations, and search update from that record state.

    inspect events →

finding.noted · reviewer:will-blair · 1 day

renders the record as of vev_d199cb2e · 1,338 events · hub

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