Pith Number

pith:J6SMLPYY

pith:2023:J6SMLPYY7CQOFALJEM6I7F7TMH

not attested not anchored not stored refs pending

Structure of lower tails in sparse random graphs

Byron Chin

arxiv:2312.12673 v2 · 2023-12-20 · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{J6SMLPYY7CQOFALJEM6I7F7TMH}

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

Lower tails for triangles inside the critical window

Receipt and verification

First computed	2026-07-05T09:57:38.775085Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4fa4c5bf18f8a0e28169233c8f97f361fbbbe370e5dcf09048d5c9c4dd4c56e7

Aliases

arxiv: 2312.12673 · arxiv_version: 2312.12673v2 · doi: 10.48550/arxiv.2312.12673 · pith_short_12: J6SMLPYY7CQO · pith_short_16: J6SMLPYY7CQOFALJ · pith_short_8: J6SMLPYY

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/J6SMLPYY7CQOFALJEM6I7F7TMH \
  | 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: 4fa4c5bf18f8a0e28169233c8f97f361fbbbe370e5dcf09048d5c9c4dd4c56e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72cceacf8c6488bf93b8fc1f31fc2a7f6a9786a2d927ac452220674b36c8c616",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-12-20T00:08:41Z",
    "title_canon_sha256": "290a7ff28c87b70958be5b2fe86e7aa3aed4d9724b8fcedac107d2cc073e50a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2312.12673",
    "kind": "arxiv",
    "version": 2
  }
}