Pith Number

pith:SOJ4U6Q6

pith:2012:SOJ4U6Q6FWH67NE2BH3HFKOMCQ

not attested not anchored not stored refs pending

Non-reversibility and self-joinings of higher orders for ergodic flows

J. Kulaga, K. Fraczek, M. Lemanczyk

arxiv:1206.3053 v2 · 2012-06-14 · 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{SOJ4U6Q6FWH67NE2BH3HFKOMCQ}

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	2026-05-18T02:52:12.924649Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9393ca7a1e2d8fefb49a09f672a9cc14256630ba0e6f7cf2fa9a14654449882e

Aliases

arxiv: 1206.3053 · arxiv_version: 1206.3053v2 · doi: 10.48550/arxiv.1206.3053 · pith_short_12: SOJ4U6Q6FWH6 · pith_short_16: SOJ4U6Q6FWH67NE2 · pith_short_8: SOJ4U6Q6

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/SOJ4U6Q6FWH67NE2BH3HFKOMCQ \
  | 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: 9393ca7a1e2d8fefb49a09f672a9cc14256630ba0e6f7cf2fa9a14654449882e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1970490cb25a4b5fab775744f310310d1aaee2157f89f525e97f3a2a507ae9b8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-06-14T09:41:12Z",
    "title_canon_sha256": "ef0fefcc925ad3d4b86cf005a6a48776611687cc538a117b0f26a17d5e61166f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.3053",
    "kind": "arxiv",
    "version": 2
  }
}