Pith Number

pith:ZPFAZ4BG

pith:2014:ZPFAZ4BGJGJJLLRPJ7TOOAW3YV

not attested not anchored not stored refs pending

Periodic billiard trajectories and Morse theory on loop spaces

Kei Irie

arxiv:1403.1953 v1 · 2014-03-08 · math.DS · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZPFAZ4BGJGJJLLRPJ7TOOAW3YV}

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	2026-05-18T02:56:51.200189Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbca0cf026499295ae2f4fe6e702dbc54179f44d5838b1ed58994bda57427f77

Aliases

arxiv: 1403.1953 · arxiv_version: 1403.1953v1 · doi: 10.48550/arxiv.1403.1953 · pith_short_12: ZPFAZ4BGJGJJ · pith_short_16: ZPFAZ4BGJGJJLLRP · pith_short_8: ZPFAZ4BG

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/ZPFAZ4BGJGJJLLRPJ7TOOAW3YV \
  | 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: cbca0cf026499295ae2f4fe6e702dbc54179f44d5838b1ed58994bda57427f77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "faf2280653adf84e5545cdc42f51fc2e8d50964199d945051b156223d89daebb",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2014-03-08T09:31:04Z",
    "title_canon_sha256": "f9c72654cf1bba4f818fec445682293d725754c0a3b72f75156a67e5dc16f508"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1403.1953",
    "kind": "arxiv",
    "version": 1
  }
}