frontiers / frontier

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

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

Finding bundle

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The h-squared-dissociated set construction needed for the polynomial bound has diameter polynomial in k, replacing geometric components in the original construction.

id: vf_3bde881fed68d7dd
frontier: Additive combinatorics: Sidon sets and N(h,k) bounds
version: 1
confidence: 0.40

1contested

file

/frontier/sidon-sets/at/vev_37fde12745314ba6permalink · after_hash 8696aff01d4321f0…

vf_3bde881fed68d7dd · sidon-sets · snapshot sha256:8badc78d64f9cdb5b9e9594b0e2855d9295d4b99abf972db104f3b417fa630af · https://vela-site-next.fly.dev/frontier/sidon-sets/at/vev_37fde12745314ba6

cite

raw json · vf_3bde881fed68d7dd (2.0 KB)

machine twin · index.json

{
 "assertion": {
  "direction": null,
  "entities": [],
  "relation": null,
  "text": "The h-squared-dissociated set construction needed for the polynomial bound has diameter polynomial in k, replacing geometric components in the original construction.",
  "type": "theoretical"
 },
 "conditions": {
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  "human_data": false,
  "in_vitro": false,
  "in_vivo": false,
  "species_unverified": [],
  "species_verified": [],
  "text": "Manually added finding; requires evidence review before scientific use."
 },
 "confidence": {
  "basis": "operator-supplied frontier prior; review required",
  "extraction_confidence": 1,
  "kind": "frontier_epistemic",
  "method": "expert_judgment",
  "score": 0.4
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 "created": "2026-05-09T19:20:35.223077+00:00",
 "evidence": {
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  "evidence_spans": [],
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  "model_system": "",
  "p_value": null,
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 "flags": {
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  "gravity_well": false,
  "negative_space": false,
  "retracted": false,
  "review_state": "needs_revision"
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 "id": "vf_3bde881fed68d7dd",
 "links": [],
 "previous_version": null,
 "provenance": {
  "authors": [
   {
    "name": "agent:research-bot-2026-05-09",
    "orcid": null
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  "citation_count": null,
  "doi": null,
  "extraction": {
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  "year": null
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Unsealed — 0 attachment(s) on record, awaiting independent verification.

0 attachments · 0 distinct checker actors · 0 methods

blame · custody trail

produced byagent:research-bot-2026-05-09finding.asserted · 2026-05-09vev_bafff34df7ac6c1c

checked byno verifier attachment on record

accepted byreviewer:will-blairfinding.reviewed · 2026-05-09vev_22c1fb678f86bdbb

history · 2 events

e3/33finding.assertedagent:research-bot-2026-05-092026-05-09→ff6ff7a864e4/33finding.reviewedreviewer:will-blair2026-05-09→8696aff01d

record state

frontier-owned

Review status

under review

finding statement

finding type

theoretical

No entity list is declared.

evidence

source-bound

1 atoms

theoretical · manual state transition

proof impact

packet context

2 events

2 reviewable changes and 0 evaluation records are attached to this finding id.

evidence

method

manual state transition

evidence type

theoretical

conditions

species_unverified
species_verified
text: Manually added finding; requires evidence review before scientific use.

provenance

source title

ChatGPT-5.5-Pro session, 2026-05-08, ~2 hours guided

authors

agent:research-bot-2026-05-09

Source records

source record

synthetic

ChatGPT-5.5-Pro session, 2026-05-08, ~2 hours guided

vs_0339f84349ab29ec

title:ChatGPT-5.5-Pro session, 2026-05-08, ~2 hours guided

manual_curation

Evidence atoms

vea_9a3732d508ed2861theoretical · unknown
The h-squared-dissociated set construction needed for the polynomial bound has diameter polynomial in k, replacing geometric components in the original construction.
vs_0339f84349ab29ec · manual_curation

Typed links

outgoing

No outgoing links.

incoming

No incoming links.

Review, event, and evaluation records

events

vev_22c1fb678f86bdbbfinding.reviewed
Bound and construction look correct under the Nathanson hypothesis but I want a Lean stub before promoting to accepted-core. The proof step that reduces geometric to polynomial diameter needs an explicit witness.
reviewer:will-blair · 2026-05-09
vev_bafff34df7ac6c1cfinding.asserted
Manual finding added to frontier state
agent:research-bot-2026-05-09 · 2026-05-09

reviewable changes

vpr_48072f346e09665ffinding.add
Manual finding added to frontier state
applied · agent:research-bot-2026-05-09 · 2026-05-09
vpr_6908c4cf64f0f4bafinding.review
Bound and construction look correct under the Nathanson hypothesis but I want a Lean stub before promoting to accepted-core. The proof step that reduces geometric to polynomial diameter needs an explicit witness.
applied · reviewer:will-blair · 2026-05-09

evaluations

No evaluation record targets this finding id.

Review status

theoretical

1 atoms

2 events

Source records

ChatGPT-5.5-Pro session, 2026-05-08, ~2 hours guided

Evidence atoms

Typed links

Review, event, and evaluation records

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