Pith Number

pith:MKDVURPE

pith:2009:MKDVURPEKWALTUUXCK5YSMYZOY

not attested not anchored not stored refs pending

Spectral flow, index and the signature operator

Charlotte Wahl, Sara Azzali

arxiv:0911.2862 v1 · 2009-11-15 · math.DG · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MKDVURPEKWALTUUXCK5YSMYZOY}

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	2026-05-18T04:23:23.289281Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62875a45e45580b9d29712bb89331976338e2054f62ceb6a85985c8d50e14202

Aliases

arxiv: 0911.2862 · arxiv_version: 0911.2862v1 · doi: 10.48550/arxiv.0911.2862 · pith_short_12: MKDVURPEKWAL · pith_short_16: MKDVURPEKWALTUUX · pith_short_8: MKDVURPE

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/MKDVURPEKWALTUUXCK5YSMYZOY \
  | 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: 62875a45e45580b9d29712bb89331976338e2054f62ceb6a85985c8d50e14202

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "81688f90a67131cc6bfe86a6fcd86a93b432f2b3e89cf9034d1e51c2a0c185ff",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-11-15T12:52:33Z",
    "title_canon_sha256": "63d2cf3106eb701db762cb4330d5300028ebb2847818ce68ec2c7952637a6cec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.2862",
    "kind": "arxiv",
    "version": 1
  }
}