Pith Number

pith:VIYYWCKZ

pith:2013:VIYYWCKZ34TB2YHAKIWXFSWHNI

not attested not anchored not stored refs pending

On caustics by reflection of algebraic surfaces

Alfrederic Josse (LM), Francoise Pene (LM)

arxiv:1304.3883 v2 · 2013-04-14 · 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{VIYYWCKZ34TB2YHAKIWXFSWHNI}

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	2026-05-18T02:49:02.064855Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa318b0959df261d60e0522d72cac76a3acbba25d0e8ee661c22436ca8bec40f

Aliases

arxiv: 1304.3883 · arxiv_version: 1304.3883v2 · doi: 10.48550/arxiv.1304.3883 · pith_short_12: VIYYWCKZ34TB · pith_short_16: VIYYWCKZ34TB2YHA · pith_short_8: VIYYWCKZ

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/VIYYWCKZ34TB2YHAKIWXFSWHNI \
  | 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: aa318b0959df261d60e0522d72cac76a3acbba25d0e8ee661c22436ca8bec40f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd457fdddf98c97917050b94445e99312498666014e71e42efb134574a539085",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2013-04-14T05:55:05Z",
    "title_canon_sha256": "1facc666041a14364c7e3aab2b509882c624bd4c2be4c2d8ff0f5ae062bb2ddd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.3883",
    "kind": "arxiv",
    "version": 2
  }
}