Pith Number

pith:ZPIJAL6P

pith:2005:ZPIJAL6PRPAXTIDD36IACKBGDO

not attested not anchored not stored refs pending

The neighborhood complex of a random graph

Matthew Kahle

arxiv:math/0512077 v4 · 2005-12-04 · math.CO · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZPIJAL6PRPAXTIDD36IACKBGDO}

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	2026-05-18T04:40:33.040217Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbd0902fcf8bc179a063df900128261b885b481225f12a16785285b746338727

Aliases

arxiv: math/0512077 · arxiv_version: math/0512077v4 · doi: 10.48550/arxiv.math/0512077 · pith_short_12: ZPIJAL6PRPAX · pith_short_16: ZPIJAL6PRPAXTIDD · pith_short_8: ZPIJAL6P

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/ZPIJAL6PRPAXTIDD36IACKBGDO \
  | 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: cbd0902fcf8bc179a063df900128261b885b481225f12a16785285b746338727

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "58ea5237ccfccf2d6234de4cdc00094591a568316c7b2bbe5ff1366befac6bdb",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2005-12-04T07:16:35Z",
    "title_canon_sha256": "60e15b5472712d4669ec9c1e963f83017fe3749e8c7467a664fb954ac88d3cc7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0512077",
    "kind": "arxiv",
    "version": 4
  }
}