Pith Number

pith:32VFUKSR

pith:2011:32VFUKSRXZUKJPMWIPQSQDV4KQ

not attested not anchored not stored refs pending

Propagation of singularities around a Lagrangian submanifold of radial points

Andr\'as Vasy, Nick Haber

arxiv:1110.1419 v1 · 2011-10-07 · math.AP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{32VFUKSRXZUKJPMWIPQSQDV4KQ}

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	2026-05-18T01:09:25.240574Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

deaa5a2a51be68a4bd9643e1280ebc543ce33216838a1fc992eab67cf886c8d2

Aliases

arxiv: 1110.1419 · arxiv_version: 1110.1419v1 · doi: 10.48550/arxiv.1110.1419 · pith_short_12: 32VFUKSRXZUK · pith_short_16: 32VFUKSRXZUKJPMW · pith_short_8: 32VFUKSR

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/32VFUKSRXZUKJPMWIPQSQDV4KQ \
  | 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: deaa5a2a51be68a4bd9643e1280ebc543ce33216838a1fc992eab67cf886c8d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "144c78117d330f1a054fde73575b2295a6d9d0fce218f6b839f3caa41ed8c6af",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-10-07T00:53:45Z",
    "title_canon_sha256": "436596df93963e83b05803b4e85d9c0af6c526c4cc6a4e1e702ec666f986dc75"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.1419",
    "kind": "arxiv",
    "version": 1
  }
}