Pith Number

pith:VTQX6EE4

pith:2015:VTQX6EE4TPYRK3HHOF5F4ZFWAX

not attested not anchored not stored refs pending

Minimum spanning acycle and lifetime of persistent homology in the Linial-Meshulam process

Tomoyuki Shirai, Yasuaki Hiraoka

arxiv:1503.05669 v1 · 2015-03-19 · math.PR · math.AT · 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{VTQX6EE4TPYRK3HHOF5F4ZFWAX}

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	2026-05-18T02:20:58.438340Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ace17f109c9bf1156ce7717a5e64b605d052f34403d8dd2f4f9c9ea67b78d6de

Aliases

arxiv: 1503.05669 · arxiv_version: 1503.05669v1 · doi: 10.48550/arxiv.1503.05669 · pith_short_12: VTQX6EE4TPYR · pith_short_16: VTQX6EE4TPYRK3HH · pith_short_8: VTQX6EE4

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/VTQX6EE4TPYRK3HHOF5F4ZFWAX \
  | 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: ace17f109c9bf1156ce7717a5e64b605d052f34403d8dd2f4f9c9ea67b78d6de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c346ad43f4e588840a8806a73e2a2dbc1547210fcd2c86c423f937acd2f5b668",
    "cross_cats_sorted": [
      "math.AT",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-03-19T08:16:30Z",
    "title_canon_sha256": "e04601fb62bc1bfb03befcc01bc5f42a035f748dec83371261e89558006754a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.05669",
    "kind": "arxiv",
    "version": 1
  }
}