Pith Number

pith:3KSJW5DK

pith:2012:3KSJW5DKJREVGF4P6Z5IFOL33Y

not attested not anchored not stored refs pending

The Wigner caustic on shell and singularities of odd functions

Miriam Manoel, Pedro de M. Rios, Wojciech Domitrz

arxiv:1207.1068 v3 · 2012-07-04 · math-ph · math.MP · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3KSJW5DKJREVGF4P6Z5IFOL33Y}

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	2026-05-18T02:37:43.111463Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

daa49b746a4c4953178ff67a82b97bde3c5e8c2f2ea066b8691b742ae2b87125

Aliases

arxiv: 1207.1068 · arxiv_version: 1207.1068v3 · doi: 10.48550/arxiv.1207.1068 · pith_short_12: 3KSJW5DKJREV · pith_short_16: 3KSJW5DKJREVGF4P · pith_short_8: 3KSJW5DK

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/3KSJW5DKJREVGF4P6Z5IFOL33Y \
  | 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: daa49b746a4c4953178ff67a82b97bde3c5e8c2f2ea066b8691b742ae2b87125

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc830cfbc6a78650d5158b0f6caf1900a6935abe7350e2232a48c703370bb9b0",
    "cross_cats_sorted": [
      "math.MP",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-07-04T18:08:47Z",
    "title_canon_sha256": "4197844eff33bd7dbb0c4f72323a346b7336c51dc0369e50dc2a8be870806e92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.1068",
    "kind": "arxiv",
    "version": 3
  }
}