Pith Number

pith:Z7M4QDHK

pith:2010:Z7M4QDHKGT45OYUAZXE3QXEISW

not attested not anchored not stored refs pending

Zeno-line, Binodal, T-{\rho} Diagram and Clusters as a new Bose-Condensate Bases on New Global Distributions in Number Theory

V.P. Maslov

arxiv:1007.4182 v3 · 2010-07-23 · math-ph · cond-mat.soft · cond-mat.stat-mech · math.MP · physics.atm-clus

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z7M4QDHKGT45OYUAZXE3QXEISW}

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	2026-05-18T04:32:33.839038Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cfd9c80cea34f9d76280cdc9b85c88959fce35e99ecb72f63f780485396aa47d

Aliases

arxiv: 1007.4182 · arxiv_version: 1007.4182v3 · doi: 10.48550/arxiv.1007.4182 · pith_short_12: Z7M4QDHKGT45 · pith_short_16: Z7M4QDHKGT45OYUA · pith_short_8: Z7M4QDHK

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/Z7M4QDHKGT45OYUAZXE3QXEISW \
  | 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: cfd9c80cea34f9d76280cdc9b85c88959fce35e99ecb72f63f780485396aa47d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c22ca0b62bc96faad7236472e0d9965e1181f79f68a94600644473627bf54f5",
    "cross_cats_sorted": [
      "cond-mat.soft",
      "cond-mat.stat-mech",
      "math.MP",
      "physics.atm-clus"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-07-23T17:35:02Z",
    "title_canon_sha256": "69f9a674219c061a0835eacafa11dd16b4189bf344e05acd48977bc6d1107d14"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.4182",
    "kind": "arxiv",
    "version": 3
  }
}