Pith Number

pith:NWNKYVIB

pith:2008:NWNKYVIBQYXOPDBL4U25ZWRYBE

not attested not anchored not stored refs pending

The volume of a differentiable stack

Alan Weinstein

arxiv:0809.2130 v3 · 2008-09-12 · math.DG · 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{NWNKYVIBQYXOPDBL4U25ZWRYBE}

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	2026-05-18T02:15:34.753451Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d9aac5501862ee78c2be535dcda38093bdbffb33e0bf43ce9757bd55945702a

Aliases

arxiv: 0809.2130 · arxiv_version: 0809.2130v3 · doi: 10.48550/arxiv.0809.2130 · pith_short_12: NWNKYVIBQYXO · pith_short_16: NWNKYVIBQYXOPDBL · pith_short_8: NWNKYVIB

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/NWNKYVIBQYXOPDBL4U25ZWRYBE \
  | 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: 6d9aac5501862ee78c2be535dcda38093bdbffb33e0bf43ce9757bd55945702a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c5ffbdd412ba207b4ddc48ba229151dbde3569634df6d3aca17f8a63c170a8e",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2008-09-12T03:55:50Z",
    "title_canon_sha256": "d7348af22a991ceedad4117d14a7397b475d5f3cf6b38772a8783ff94269386d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0809.2130",
    "kind": "arxiv",
    "version": 3
  }
}