Pith Number

pith:ZTR5KR4R

pith:2006:ZTR5KR4RPG53UCECJMFITTDTXD

not attested not anchored not stored refs pending

Fourier's Law from Closure Equations

Antti Kupiainen, Jean Bricmont

arxiv:math-ph/0609002 v1 · 2006-09-01 · 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{ZTR5KR4RPG53UCECJMFITTDTXD}

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

Phonon Gravity, Non-equilibrium QFT, and the Tolman Thermal Equivalence Principle

Receipt and verification

First computed	2026-07-04T17:02:07.050245Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cce3d5479179bbba08824b0a89cc73b8e609659bf886924a9fa1c1cc62e391dc

Aliases

arxiv: math-ph/0609002 · arxiv_version: math-ph/0609002v1 · doi: 10.48550/arxiv.math-ph/0609002 · pith_short_12: ZTR5KR4RPG53 · pith_short_16: ZTR5KR4RPG53UCEC · pith_short_8: ZTR5KR4R

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/ZTR5KR4RPG53UCECJMFITTDTXD \
  | 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: cce3d5479179bbba08824b0a89cc73b8e609659bf886924a9fa1c1cc62e391dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "edb97d8121ca64d58ab248e63039f1e062584cf86a292ebc8176441b9aaa5197",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2006-09-01T07:15:16Z",
    "title_canon_sha256": "6313fc088a85ccb58b233444b4684a2913fc8578cce8878a181f06a4532bc62e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0609002",
    "kind": "arxiv",
    "version": 1
  }
}