Pith Number

pith:4WHNDZSQ

pith:2012:4WHNDZSQQ7DN3KGTSJHP42F4Z3

not attested not anchored not stored refs pending

Quantum Ergodicity for a Class of Mixed Systems

Jeffrey Galkowski

arxiv:1209.2968 v6 · 2012-09-13 · math-ph · math.AP · math.MP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4WHNDZSQQ7DN3KGTSJHP42F4Z3}

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	2026-05-18T02:48:43.739686Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e58ed1e65087c6dda8d3924efe68bccecd9fd7ba118ba59b2ece10fd5b307296

Aliases

arxiv: 1209.2968 · arxiv_version: 1209.2968v6 · doi: 10.48550/arxiv.1209.2968 · pith_short_12: 4WHNDZSQQ7DN · pith_short_16: 4WHNDZSQQ7DN3KGT · pith_short_8: 4WHNDZSQ

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/4WHNDZSQQ7DN3KGTSJHP42F4Z3 \
  | 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: e58ed1e65087c6dda8d3924efe68bccecd9fd7ba118ba59b2ece10fd5b307296

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6984a04b4e5edc15f4825103fe19b34b43cc08ddba57d5a44a16a0c2f1b021ed",
    "cross_cats_sorted": [
      "math.AP",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-09-13T17:26:36Z",
    "title_canon_sha256": "87d7b27e6ed6b2bd257ea9f5c3fdcce5938b3411af4ee5b546bbc9af474d2560"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.2968",
    "kind": "arxiv",
    "version": 6
  }
}