Pith Number

pith:6ATQX45G

pith:2022:6ATQX45GWWKYK7XBXQQDEDJA25

not attested not anchored not stored refs pending

A proof of finite crystallization via stratification

Leonard Kreutz, Manuel Friedrich

arxiv:2209.14880 v3 · 2022-09-29 · cond-mat.mes-hall · math-ph · math.AP · 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{6ATQX45GWWKYK7XBXQQDEDJA25}

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	2026-07-05T06:42:57.140859Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f0270bf3a6b595857ee1bc20320d20d74db5780e1fce2687aea7495448281dea

Aliases

arxiv: 2209.14880 · arxiv_version: 2209.14880v3 · doi: 10.48550/arxiv.2209.14880 · pith_short_12: 6ATQX45GWWKY · pith_short_16: 6ATQX45GWWKYK7XB · pith_short_8: 6ATQX45G

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/6ATQX45GWWKYK7XBXQQDEDJA25 \
  | 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: f0270bf3a6b595857ee1bc20320d20d74db5780e1fce2687aea7495448281dea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80a630f8f5a7d40833d7b304b4f3272ac02ecdb1547937a11354602cbf96ae11",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.mes-hall",
    "submitted_at": "2022-09-29T15:48:46Z",
    "title_canon_sha256": "4e516c00da8bd304a7601310fa6587d3501e09d2f5d244c3a2fe6fa03d416860"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2209.14880",
    "kind": "arxiv",
    "version": 3
  }
}