Pith Number

pith:2CPZ5EYM

pith:2012:2CPZ5EYMG7FJBVRZTLD6LLRRBL

not attested not anchored not stored refs pending

On index expectation and curvature for networks

Oliver Knill

arxiv:1202.4514 v1 · 2012-02-21 · math.DG · cs.DM · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2CPZ5EYMG7FJBVRZTLD6LLRRBL}

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.

Cited by

1 paper in Pith

The energy of a simplicial complex

Receipt and verification

First computed	2026-05-18T04:01:50.456228Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d09f9e930c37ca90d6399ac7e5ae310ac68e055eac5c8cbe2a366d39806113f6

Aliases

arxiv: 1202.4514 · arxiv_version: 1202.4514v1 · doi: 10.48550/arxiv.1202.4514 · pith_short_12: 2CPZ5EYMG7FJ · pith_short_16: 2CPZ5EYMG7FJBVRZ · pith_short_8: 2CPZ5EYM

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/2CPZ5EYMG7FJBVRZTLD6LLRRBL \
  | 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: d09f9e930c37ca90d6399ac7e5ae310ac68e055eac5c8cbe2a366d39806113f6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47fbb929c4ac690e63bc904d2fcd3ac3da37737b282bc37298e82643eba887e1",
    "cross_cats_sorted": [
      "cs.DM",
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-02-21T02:27:55Z",
    "title_canon_sha256": "23d74b57ed177fa4caf7c9ad31913edcac516eecd56d169abcccb6a3345a04dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.4514",
    "kind": "arxiv",
    "version": 1
  }
}