Pith Number

pith:UESY5Z26

pith:2012:UESY5Z26ITRU6YHUSZDXKV3LYF

not attested not anchored not stored refs pending

On the class of caustics by reflection

Alfrederic Josse (LM), Francoise Pene (LM)

arxiv:1210.6551 v2 · 2012-10-24 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UESY5Z26ITRU6YHUSZDXKV3LYF}

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	2026-05-18T03:28:05.539078Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a1258ee75e44e34f60f4964775576bc17d76ef09115d4a9cd119e641aca8bad8

Aliases

arxiv: 1210.6551 · arxiv_version: 1210.6551v2 · doi: 10.48550/arxiv.1210.6551 · pith_short_12: UESY5Z26ITRU · pith_short_16: UESY5Z26ITRU6YHU · pith_short_8: UESY5Z26

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/UESY5Z26ITRU6YHUSZDXKV3LYF \
  | 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: a1258ee75e44e34f60f4964775576bc17d76ef09115d4a9cd119e641aca8bad8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b1847c9c336d9df1a80ef8c1bb124ae16f4183ecca19fab7ec0db7b68f79814",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-10-24T14:47:38Z",
    "title_canon_sha256": "3d018c8810abd1e01755ccd88b942081b4261a33a6f6d9158cd19bf37560f815"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.6551",
    "kind": "arxiv",
    "version": 2
  }
}