Pith Number

pith:TLY4UWJF

pith:2010:TLY4UWJFZ5AWTP4RRCA42YTJJT

not attested not anchored not stored refs pending

Invisibility in billiards

Alexander Plakhov, Vera Roshchina

arxiv:1009.1104 v1 · 2010-09-06 · 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{TLY4UWJFZ5AWTP4RRCA42YTJJT}

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	2026-05-18T02:05:36.143775Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9af1ca5925cf4169bf918881cd62694cdef6c445d5a5865908303b242bec3a0a

Aliases

arxiv: 1009.1104 · arxiv_version: 1009.1104v1 · doi: 10.48550/arxiv.1009.1104 · pith_short_12: TLY4UWJFZ5AW · pith_short_16: TLY4UWJFZ5AWTP4R · pith_short_8: TLY4UWJF

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/TLY4UWJFZ5AWTP4RRCA42YTJJT \
  | 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: 9af1ca5925cf4169bf918881cd62694cdef6c445d5a5865908303b242bec3a0a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eca4dd7fddeb284e0d389d24585bffb526711c797cb62699d21ad3bc2a410842",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-09-06T17:47:10Z",
    "title_canon_sha256": "b5dc400f1548071fd08315d89115f41102f2f610be74e9937a15e7f4b0921763"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.1104",
    "kind": "arxiv",
    "version": 1
  }
}