Pith Number

pith:TYGXTCKI

pith:2012:TYGXTCKIHNL553FORMY2ET5IRD

not attested not anchored not stored refs pending

Fundamental Groups of Random Clique Complexes

Eric Babson

arxiv:1207.5028 v2 · 2012-07-20 · math.CO · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TYGXTCKIHNL553FORMY2ET5IRD}

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

When does a tree activate the random graph?

Receipt and verification

First computed	2026-05-18T03:33:25.859024Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e0d7989483b57deecae8b31a24fa888fae745c31f91c43a992ed98fda32cdee

Aliases

arxiv: 1207.5028 · arxiv_version: 1207.5028v2 · doi: 10.48550/arxiv.1207.5028 · pith_short_12: TYGXTCKIHNL5 · pith_short_16: TYGXTCKIHNL553FO · pith_short_8: TYGXTCKI

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/TYGXTCKIHNL553FORMY2ET5IRD \
  | 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: 9e0d7989483b57deecae8b31a24fa888fae745c31f91c43a992ed98fda32cdee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48d343d72fceb4bb49ee388734a6f452ff85a84e1c09ca1af61513ecae2d7b47",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-07-20T19:10:41Z",
    "title_canon_sha256": "fd0674f297672dc6ea06016d01692e7e33fef555eb99b1a8d96eca01cdc7a413"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.5028",
    "kind": "arxiv",
    "version": 2
  }
}