Pith Number

pith:URNOBDM2

pith:2019:URNOBDM2FKCRY4IJ3GLSHF2R3T

not attested not anchored not stored refs pending

From Sharma-Mittal to von-Neumann Entropy of a Graph

Amrik Singh, Partha Guha, Sandeep Kumar Yadav, Souma Mazumdar, Supriyo Dutta

arxiv:1902.07548 v1 · 2019-02-20 · cs.DM · cond-mat.dis-nn · cs.IT · math.CO · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{URNOBDM2FKCRY4IJ3GLSHF2R3T}

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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.

Cited by

1 paper in Pith

The Sharma-Mittal Entropy is Subadditive and Supermodular on the Majorization Lattice

Receipt and verification

First computed	2026-05-17T23:53:07.535726Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a45ae08d9a2a851c7109d997239751dce8d0e4991176976eda3127300dd58507

Aliases

arxiv: 1902.07548 · arxiv_version: 1902.07548v1 · doi: 10.48550/arxiv.1902.07548 · pith_short_12: URNOBDM2FKCR · pith_short_16: URNOBDM2FKCRY4IJ · pith_short_8: URNOBDM2

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/URNOBDM2FKCRY4IJ3GLSHF2R3T \
  | 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: a45ae08d9a2a851c7109d997239751dce8d0e4991176976eda3127300dd58507

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "634ed033d92eb8b198e2776726e24396f4c3b5424d10f82ab0d88fb66b6bc268",
    "cross_cats_sorted": [
      "cond-mat.dis-nn",
      "cs.IT",
      "math.CO",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2019-02-20T13:15:09Z",
    "title_canon_sha256": "fb37507369c4acde23541b375c7afc33f746c3c9c8eddc9a068c7235b4921df2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.07548",
    "kind": "arxiv",
    "version": 1
  }
}