Pith Number

pith:2DFP7Z6I

pith:2004:2DFP7Z6ILCZTWYKNP3LHDJHG3K

not attested not anchored not stored refs pending

An asymptotic formula for models with caustics

T. Sakaguchi

arxiv:math-ph/0412020 v1 · 2004-12-08 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2DFP7Z6ILCZTWYKNP3LHDJHG3K}

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	2026-07-04T14:34:03.902239Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d0caffe7c858b33b614d7ed671a4e6da9f6ad698e94bc14ecc2de46c64085af5

Aliases

arxiv: math-ph/0412020 · arxiv_version: math-ph/0412020v1 · doi: 10.48550/arxiv.math-ph/0412020 · pith_short_12: 2DFP7Z6ILCZT · pith_short_16: 2DFP7Z6ILCZTWYKN · pith_short_8: 2DFP7Z6I

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/2DFP7Z6ILCZTWYKNP3LHDJHG3K \
  | 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: d0caffe7c858b33b614d7ed671a4e6da9f6ad698e94bc14ecc2de46c64085af5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a373abd2572fbadd1d3271fdb1c0aef0e86f6f2744e46b7a24ce1b89dc47292",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2004-12-08T01:37:27Z",
    "title_canon_sha256": "e50fec329ed52b6ced58d855346fbe1d3180bd87b97944a8c4ddf97402a6f932"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0412020",
    "kind": "arxiv",
    "version": 1
  }
}