Pith Number

pith:JWM4CU7E

pith:2007:JWM4CU7EL3Y2R25WUK2A6PD5B2

not attested not anchored not stored refs pending

Structure and randomness in combinatorics

Terence Tao

arxiv:0707.4269 v2 · 2007-07-29 · 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{JWM4CU7EL3Y2R25WUK2A6PD5B2}

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	2026-05-18T04:09:15.361852Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4d99c153e45ef1a8ebb6a2b40f3c7d0eb486cdf320508a6a4463c3f1773f336c

Aliases

arxiv: 0707.4269 · arxiv_version: 0707.4269v2 · doi: 10.48550/arxiv.0707.4269 · pith_short_12: JWM4CU7EL3Y2 · pith_short_16: JWM4CU7EL3Y2R25W · pith_short_8: JWM4CU7E

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/JWM4CU7EL3Y2R25WUK2A6PD5B2 \
  | 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: 4d99c153e45ef1a8ebb6a2b40f3c7d0eb486cdf320508a6a4463c3f1773f336c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8555f50b8c491f6e70ff6732479696cfbc088d7bc0cbaf6da6fe15a11ebee919",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2007-07-29T00:47:53Z",
    "title_canon_sha256": "ddc4983f71287bd34c9a9d7ef451816ac4e070c427179e436546076946b57d21"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0707.4269",
    "kind": "arxiv",
    "version": 2
  }
}