Pith Number

pith:53QFD5BF

pith:2011:53QFD5BFVPCETDOVXKPZXYLRZQ

not attested not anchored not stored refs pending

The ghost length and duality on the chain and cochain type levels

Katsuhiko Kuribayashi

arxiv:1108.3890 v3 · 2011-08-19 · math.AT · math.RA · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{53QFD5BFVPCETDOVXKPZXYLRZQ}

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	2026-05-18T01:22:03.660289Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eee051f425abc4498dd5ba9f9be171cc13aac2fb0bbce8352e2a9e027e8583ea

Aliases

arxiv: 1108.3890 · arxiv_version: 1108.3890v3 · doi: 10.48550/arxiv.1108.3890 · pith_short_12: 53QFD5BFVPCE · pith_short_16: 53QFD5BFVPCETDOV · pith_short_8: 53QFD5BF

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/53QFD5BFVPCETDOVXKPZXYLRZQ \
  | 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: eee051f425abc4498dd5ba9f9be171cc13aac2fb0bbce8352e2a9e027e8583ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9df8632d31e9a3b59822ed0fce58835e039102d324314c42fb1c5177229113df",
    "cross_cats_sorted": [
      "math.RA",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2011-08-19T04:14:14Z",
    "title_canon_sha256": "068d97354ecb99d8b00b79663ce0a7570523eb515d29452ece45f4bd47151848"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.3890",
    "kind": "arxiv",
    "version": 3
  }
}