Pith Number

pith:4AIVPJVK

pith:2025:4AIVPJVKVYPLKZO2MV3TU5IAVS

not attested not anchored not stored refs pending

From Barcode Entropy to Metric Entropy

Basak Z. Gurel, Erman Cineli, Viktor L. Ginzburg

arxiv:2507.13215 v2 · 2025-07-17 · math.SG · 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{4AIVPJVKVYPLKZO2MV3TU5IAVS}

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	2026-06-12T01:09:11.024754Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e01157a6aaae1eb565da65773a7500ac82352b18055e57d1f330f21a8e003e5c

Aliases

arxiv: 2507.13215 · arxiv_version: 2507.13215v2 · doi: 10.48550/arxiv.2507.13215 · pith_short_12: 4AIVPJVKVYPL · pith_short_16: 4AIVPJVKVYPLKZO2 · pith_short_8: 4AIVPJVK

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/4AIVPJVKVYPLKZO2MV3TU5IAVS \
  | 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: e01157a6aaae1eb565da65773a7500ac82352b18055e57d1f330f21a8e003e5c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b015ed9547eb18d3ba489ae7424f9006ff23f1fe97e4dfccc1239afa03f19bee",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2025-07-17T15:21:59Z",
    "title_canon_sha256": "86f725534fdb7259e2f6d3b217307cf6381bfa832e0a1355fb8c211689dcb854"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.13215",
    "kind": "arxiv",
    "version": 2
  }
}