Pith Number

pith:PA5GF5MQ

pith:2011:PA5GF5MQHI34QACOFYJOOV2BMK

not attested not anchored not stored refs pending

Entropy and Ergodic Measures for Toral Automorphisms

Peng Sun

arxiv:1103.1115 v1 · 2011-03-06 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PA5GF5MQHI34QACOFYJOOV2BMK}

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	2026-05-18T04:27:17.083265Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

783a62f5903a37c8004e2e12e7574162bb36e61611c3daec203ad8b239d4a451

Aliases

arxiv: 1103.1115 · arxiv_version: 1103.1115v1 · doi: 10.48550/arxiv.1103.1115 · pith_short_12: PA5GF5MQHI34 · pith_short_16: PA5GF5MQHI34QACO · pith_short_8: PA5GF5MQ

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/PA5GF5MQHI34QACOFYJOOV2BMK \
  | 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: 783a62f5903a37c8004e2e12e7574162bb36e61611c3daec203ad8b239d4a451

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a3739a4cd0ffb019d00826a8760ee857e0cededc296779538e3c74a61f1461e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-03-06T11:00:35Z",
    "title_canon_sha256": "bd3bbf4baf1711086bd422a27ad735aaecea3688b6d30ad64489de9a060483a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.1115",
    "kind": "arxiv",
    "version": 1
  }
}