Pith Number

pith:QL2O5RRO

pith:2011:QL2O5RRO2OIRR7Y3BXI4QCZ567

not attested not anchored not stored refs pending

Geometric Perspective of Entropy Function: Embedding, Spectrum and Convexity

Bhupendra Nath Tiwari

arxiv:1108.4654 v2 · 2011-08-23 · hep-th · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QL2O5RRO2OIRR7Y3BXI4QCZ567}

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	2026-05-18T04:14:16.256385Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82f4eec62ed39118ff1b0dd1c80b3df7cf77eef77537970f8b433ca80c2eae51

Aliases

arxiv: 1108.4654 · arxiv_version: 1108.4654v2 · doi: 10.48550/arxiv.1108.4654 · pith_short_12: QL2O5RRO2OIR · pith_short_16: QL2O5RRO2OIRR7Y3 · pith_short_8: QL2O5RRO

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/QL2O5RRO2OIRR7Y3BXI4QCZ567 \
  | 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: 82f4eec62ed39118ff1b0dd1c80b3df7cf77eef77537970f8b433ca80c2eae51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a25a39951dbc006219864082fca9ddfbb2d80c4eaa26cfb0be6929920a54ec6",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2011-08-23T16:58:25Z",
    "title_canon_sha256": "3ed657c779204780f6579ee010fd4191cf3071e330ab6cf80a1012877f014c60"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.4654",
    "kind": "arxiv",
    "version": 2
  }
}