Pith Number

pith:YE2UP3AS

pith:2023:YE2UP3ASIUNQ5SKMTEP24XIJ76

not attested not anchored not stored refs pending

Abundance: Asymmetric Graph Removal Lemmas and Integer Solutions to Linear Equations

Ant\'onio Gir\~ao, Eoin Hurley, Freddie Illingworth, Lukas Michel

arxiv:2310.18202 v1 · 2023-10-27 · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YE2UP3ASIUNQ5SKMTEP24XIJ76}

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.

Receipt and verification

First computed	2026-07-05T07:05:58.717121Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c13547ec12451b0ec94c991fae5d09ff887f5e5cdcbf4839d407451ed00175dc

Aliases

arxiv: 2310.18202 · arxiv_version: 2310.18202v1 · doi: 10.48550/arxiv.2310.18202 · pith_short_12: YE2UP3ASIUNQ · pith_short_16: YE2UP3ASIUNQ5SKM · pith_short_8: YE2UP3AS

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/YE2UP3ASIUNQ5SKMTEP24XIJ76 \
  | 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: c13547ec12451b0ec94c991fae5d09ff887f5e5cdcbf4839d407451ed00175dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6255a278dffcbfba20e73e97900972251c83bcfd8c36c8da8d7f3c59ac879d09",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-10-27T15:20:48Z",
    "title_canon_sha256": "9fffc8a4965d9cb6ee3da39177e8442f9044a2d8a6f900380c6e923c61e68711"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2310.18202",
    "kind": "arxiv",
    "version": 1
  }
}