Pith Number

pith:VEBVZD72

pith:2002:VEBVZD72OPY5DH2Z7VMEATX2MF

not attested not anchored not stored refs pending

Volume comparison and the sigma_k-Yamabe problem

Jeff Viaclovsky, Matthew Gursky

arxiv:math/0210302 v2 · 2002-10-18 · math.DG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VEBVZD72OPY5DH2Z7VMEATX2MF}

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	2026-07-04T15:48:29.223696Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9035c8ffa73f1d19f59fd58404efa617b16410b0ae5de15dea4e341d0225ee3

Aliases

arxiv: math/0210302 · arxiv_version: math/0210302v2 · doi: 10.48550/arxiv.math/0210302 · pith_short_12: VEBVZD72OPY5 · pith_short_16: VEBVZD72OPY5DH2Z · pith_short_8: VEBVZD72

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/VEBVZD72OPY5DH2Z7VMEATX2MF \
  | 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: a9035c8ffa73f1d19f59fd58404efa617b16410b0ae5de15dea4e341d0225ee3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55c6839acf3d6785ccca741166506fe9907e9e943d062377e477feebb409bc16",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2002-10-18T21:40:27Z",
    "title_canon_sha256": "7948c52890412a7bf179bc3d4a3c91b8334231face15a198f563a1bd3267c60c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0210302",
    "kind": "arxiv",
    "version": 2
  }
}