Pith Number

pith:TIGLB4ZA

pith:2025:TIGLB4ZAYGOLICPP4M3JA5JUP6

not attested not anchored not stored refs pending

On complex algebraic caustics in planar and projective billiards

Alexey Glutsyuk

arxiv:2509.11257 v1 · 2025-09-14 · 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{TIGLB4ZAYGOLICPP4M3JA5JUP6}

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	2026-07-05T12:11:36.205607Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a0cb0f320c19cb409efe3369075347fa61e66a0e228ee3d623b577933e13203

Aliases

arxiv: 2509.11257 · arxiv_version: 2509.11257v1 · doi: 10.48550/arxiv.2509.11257 · pith_short_12: TIGLB4ZAYGOL · pith_short_16: TIGLB4ZAYGOLICPP · pith_short_8: TIGLB4ZA

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/TIGLB4ZAYGOLICPP4M3JA5JUP6 \
  | 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: 9a0cb0f320c19cb409efe3369075347fa61e66a0e228ee3d623b577933e13203

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8629dccec39a57bd161c6f388e5705ceba7681e85d4ec69681d9bb98fcd6bece",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2025-09-14T12:58:25Z",
    "title_canon_sha256": "f36d9e2b6bef4cc34817319b20dddb97b92b7ff0d2f2ad42a7da049e0cd4231f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.11257",
    "kind": "arxiv",
    "version": 1
  }
}