Pith Number

pith:YKRNLQ6E

pith:2024:YKRNLQ6E6W6B2SL2YNXIRMNNBY

not attested not anchored not stored refs pending

Past and future of the cap set problem

Ernie Croot, P\'eter P\'al Pach, Vsevolod F. Lev

arxiv:2408.02328 v1 · 2024-08-05 · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YKRNLQ6E6W6B2SL2YNXIRMNNBY}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Cited by

1 paper in Pith

STRCMP: Integrating Graph Structural Priors with Language Models for Combinatorial Optimization

Receipt and verification

First computed	2026-07-05T08:52:11.366419Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c2a2d5c3c4f5bc1d497ac36e88b1ad0e091f5bf03686cfbeabe4238ab3efd876

Aliases

arxiv: 2408.02328 · arxiv_version: 2408.02328v1 · doi: 10.48550/arxiv.2408.02328 · pith_short_12: YKRNLQ6E6W6B · pith_short_16: YKRNLQ6E6W6B2SL2 · pith_short_8: YKRNLQ6E

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YKRNLQ6E6W6B2SL2YNXIRMNNBY \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c2a2d5c3c4f5bc1d497ac36e88b1ad0e091f5bf03686cfbeabe4238ab3efd876

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dca735d73adb1952b3960313253f28f2e64427a08d08296335620ff3b2cd18ac",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-08-05T09:11:52Z",
    "title_canon_sha256": "7a400d1a742006dea0b0b239d03f574169a862132e37e8b394dcfe6891c6a981"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2408.02328",
    "kind": "arxiv",
    "version": 1
  }
}