Pith Number

pith:3TOA4X7S

pith:2012:3TOA4X7SO2G5XI35EKRSEPFXZQ

not attested not anchored not stored refs pending

Widder's representation theorem for symmetric local Dirichlet spaces

Laurent Saloff-Coste, Nathaniel Eldredge

arxiv:1204.1926 v3 · 2012-04-09 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3TOA4X7SO2G5XI35EKRSEPFXZQ}

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	2026-05-18T00:41:46.882523Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dcdc0e5ff2768ddba37d22a3223cb7cc3e5be37722fe86906baf179e0c2a9c56

Aliases

arxiv: 1204.1926 · arxiv_version: 1204.1926v3 · doi: 10.48550/arxiv.1204.1926 · pith_short_12: 3TOA4X7SO2G5 · pith_short_16: 3TOA4X7SO2G5XI35 · pith_short_8: 3TOA4X7S

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/3TOA4X7SO2G5XI35EKRSEPFXZQ \
  | 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: dcdc0e5ff2768ddba37d22a3223cb7cc3e5be37722fe86906baf179e0c2a9c56

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea4f4c9f030d15897fd77eb45b3114643d9959577310738ea6cbad3cde49b64d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-04-09T17:05:50Z",
    "title_canon_sha256": "4517507826236bc38303736996ec4ac9a18bc6a25caa7360b8b848a9a2ba85d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.1926",
    "kind": "arxiv",
    "version": 3
  }
}