Pith Number

pith:2YNJMBCH

pith:2011:2YNJMBCH7KWP6AKB5PZHOQF6Q7

not attested not anchored not stored refs pending

Discrete Laplace Cycles of Period Four

Hans-Peter Schr\"ocker

arxiv:1104.3689 v1 · 2011-04-19 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2YNJMBCH7KWP6AKB5PZHOQF6Q7}

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	2026-05-18T03:58:04.606026Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d61a960447faacff0141ebf27740be87dcb8ecca793bcbe216798cd4f1ac4d40

Aliases

arxiv: 1104.3689 · arxiv_version: 1104.3689v1 · doi: 10.48550/arxiv.1104.3689 · pith_short_12: 2YNJMBCH7KWP · pith_short_16: 2YNJMBCH7KWP6AKB · pith_short_8: 2YNJMBCH

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/2YNJMBCH7KWP6AKB5PZHOQF6Q7 \
  | 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: d61a960447faacff0141ebf27740be87dcb8ecca793bcbe216798cd4f1ac4d40

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb041635b2d70fe93da9ec254828a0de58a8b24e528c08d5d9f56585859cac0d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-04-19T10:05:35Z",
    "title_canon_sha256": "b736fb5553d550af7ed489958b95c0ac5601e8ecd2fdf844ef234489401d1a66"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.3689",
    "kind": "arxiv",
    "version": 1
  }
}