Pith Number

pith:B5CVJJPK

pith:2012:B5CVJJPKT64O7TMKO2TD4AFEE6

not attested not anchored not stored refs pending

Directional complexity and entropy for lift mappings

L. Glebsky, M. Courbage, V. Afraimovich

arxiv:1212.0174 v3 · 2012-12-02 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B5CVJJPKT64O7TMKO2TD4AFEE6}

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	2026-05-18T01:04:54.298905Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f4554a5ea9fb8efcd8a76a63e00a427bec126c0fb89b1ecafa5a9ac5a195e01

Aliases

arxiv: 1212.0174 · arxiv_version: 1212.0174v3 · doi: 10.48550/arxiv.1212.0174 · pith_short_12: B5CVJJPKT64O · pith_short_16: B5CVJJPKT64O7TMK · pith_short_8: B5CVJJPK

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/B5CVJJPKT64O7TMKO2TD4AFEE6 \
  | 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: 0f4554a5ea9fb8efcd8a76a63e00a427bec126c0fb89b1ecafa5a9ac5a195e01

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b96bd09f4143c38a857661a341b49789b26097d0e1664d0102500071ef112c2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-12-02T01:37:45Z",
    "title_canon_sha256": "8e03e595cf73f3f8de68730932197ba9f4311956e6a904834dc332f7faf5de3c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.0174",
    "kind": "arxiv",
    "version": 3
  }
}