Pith Number

pith:KAPTNSPS

pith:2010:KAPTNSPSUR5ZK4E7Z7IUPUO46N

not attested not anchored not stored refs pending

Symplectic capacity and short periodic billiard trajectory

Kei Irie

arxiv:1010.3170 v2 · 2010-10-15 · math.SG · 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{KAPTNSPSUR5ZK4E7Z7IUPUO46N}

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	2026-05-18T04:03:07.266388Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

501f36c9f2a47b95709fcfd147d1dcf34c55aa5c26b866d03f72dc66b72dc531

Aliases

arxiv: 1010.3170 · arxiv_version: 1010.3170v2 · doi: 10.48550/arxiv.1010.3170 · pith_short_12: KAPTNSPSUR5Z · pith_short_16: KAPTNSPSUR5ZK4E7 · pith_short_8: KAPTNSPS

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/KAPTNSPSUR5ZK4E7Z7IUPUO46N \
  | 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: 501f36c9f2a47b95709fcfd147d1dcf34c55aa5c26b866d03f72dc66b72dc531

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7f0bca74717b1fbda74141e2ee91f7c5c6f46ec54bab7853cf3f6a257a201fc9",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2010-10-15T13:58:28Z",
    "title_canon_sha256": "c0832a32b687a8117abc78540cea3e117867172d57ad5275f44410be31aba5c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.3170",
    "kind": "arxiv",
    "version": 2
  }
}