Pith Number

pith:YBNI62JA

pith:2026:YBNI62JA4NETOY4Z6OEJYIVTSB

not attested not anchored not stored refs pending

Volume Stability for Hyperbolic Manifolds and Applications to General Relativity

Puskar Mondal, Shing-Tung Yau

arxiv:2607.27666 v1 · 2026-07-30 · math.DG · gr-qc · 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{YBNI62JA4NETOY4Z6OEJYIVTSB}

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	2026-07-31T01:29:41.083743Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

c05a8f6920e349376399f3889c22b39058e345e3ab9c9be620b1aaf15fdda077

Aliases

arxiv: 2607.27666 · arxiv_version: 2607.27666v1 · doi: 10.48550/arxiv.2607.27666 · pith_short_12: YBNI62JA4NET · pith_short_16: YBNI62JA4NETOY4Z · pith_short_8: YBNI62JA

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/YBNI62JA4NETOY4Z6OEJYIVTSB \
  | 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: c05a8f6920e349376399f3889c22b39058e345e3ab9c9be620b1aaf15fdda077

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe2c18a296b53d93a6c87794a8619ad5881a19eacfae66abfab23a3b0fc6252d",
    "cross_cats_sorted": [
      "gr-qc",
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-07-30T04:28:30Z",
    "title_canon_sha256": "4b5d4e37d1a48f434293cab8d80b872830b01b7af3515e20692fbe550259a5cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.27666",
    "kind": "arxiv",
    "version": 1
  }
}