Pith Number

pith:TXKFEBYI

pith:2013:TXKFEBYI6SSOZOWDP35X2WZ5GY

not attested not anchored not stored refs pending

Degree and class of caustics by reflection for a generic source

Alfrederic Josse (LM), Francoise Pene (LM)

arxiv:1301.1846 v1 · 2013-01-09 · 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{TXKFEBYI6SSOZOWDP35X2WZ5GY}

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	2026-05-18T03:36:55.825360Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9dd4520708f4a4ecbac37efb7d5b3d3636699f993f54fb8d56800318a9f92adb

Aliases

arxiv: 1301.1846 · arxiv_version: 1301.1846v1 · doi: 10.48550/arxiv.1301.1846 · pith_short_12: TXKFEBYI6SSO · pith_short_16: TXKFEBYI6SSOZOWD · pith_short_8: TXKFEBYI

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/TXKFEBYI6SSOZOWDP35X2WZ5GY \
  | 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: 9dd4520708f4a4ecbac37efb7d5b3d3636699f993f54fb8d56800318a9f92adb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a910934a88fff819ba00ca976c92812c9b8424168dba658ed119fd46907f4d6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2013-01-09T13:15:47Z",
    "title_canon_sha256": "51f624c4b624d54964735accb79d1ef8f4410b6da284286c09d8d0eaf071cda1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.1846",
    "kind": "arxiv",
    "version": 1
  }
}