Pith Number

pith:M475APHY

pith:2010:M475APHYN4HWGJPBCGOYR643JF

not attested not anchored not stored refs pending

Adjoint entropy vs Topological entropy

Anna Giordano Bruno

arxiv:1007.0346 v5 · 2010-07-02 · math.GN · 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{M475APHYN4HWGJPBCGOYR643JF}

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	2026-05-18T04:17:13.755482Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

673fd03cf86f0f6325e1119d88fb9b494bfba11244ec6a55d6b74db11b4c233b

Aliases

arxiv: 1007.0346 · arxiv_version: 1007.0346v5 · doi: 10.48550/arxiv.1007.0346 · pith_short_12: M475APHYN4HW · pith_short_16: M475APHYN4HWGJPB · pith_short_8: M475APHY

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/M475APHYN4HWGJPBCGOYR643JF \
  | 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: 673fd03cf86f0f6325e1119d88fb9b494bfba11244ec6a55d6b74db11b4c233b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "15dc43bf2710a69d0020ffac0c27559153a4552b0fc5241b246f12f66c692f6b",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GN",
    "submitted_at": "2010-07-02T11:58:54Z",
    "title_canon_sha256": "3d3b5107cecaebafeb9b7d3085d6fe38c8a6745d4afe0b82d2ec527ae1dd7bc9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.0346",
    "kind": "arxiv",
    "version": 5
  }
}