Pith Number

pith:Z4FU3WY4

pith:2010:Z4FU3WY4VIOC67JS3BZJS25PDB

not attested not anchored not stored refs pending

Discrete Complex Analysis and Probability

Stanislav Smirnov

arxiv:1009.6077 v1 · 2010-09-30 · math-ph · math.CV · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z4FU3WY4VIOC67JS3BZJS25PDB}

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

Harmonic morphisms and dynamical invariants in network renormalization

Receipt and verification

First computed	2026-05-18T04:40:01.103247Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf0b4ddb1caa1c2f7d32d872996baf1842f1574552c0fbc79a280aa49ab7b7c0

Aliases

arxiv: 1009.6077 · arxiv_version: 1009.6077v1 · doi: 10.48550/arxiv.1009.6077 · pith_short_12: Z4FU3WY4VIOC · pith_short_16: Z4FU3WY4VIOC67JS · pith_short_8: Z4FU3WY4

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/Z4FU3WY4VIOC67JS3BZJS25PDB \
  | 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: cf0b4ddb1caa1c2f7d32d872996baf1842f1574552c0fbc79a280aa49ab7b7c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "92c581a7efc24b56e2271be7a24fc7168924d3a25720f2e2b3031211d9d6c329",
    "cross_cats_sorted": [
      "math.CV",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-09-30T09:22:01Z",
    "title_canon_sha256": "96292cf5977bf77c37bf3fca32d678eefc38340ee8e9555d2ab1dbd03034f5c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.6077",
    "kind": "arxiv",
    "version": 1
  }
}