Pith Number

pith:2GLJWVKZ

pith:2011:2GLJWVKZSM27HZCVMZMQRB7YXE

not attested not anchored not stored refs pending

New monotonicity formulas for Ricci curvature and applications; I

Tobias Holck Colding

arxiv:1111.4715 v1 · 2011-11-21 · math.DG · math.AP · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2GLJWVKZSM27HZCVMZMQRB7YXE}

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.

Cited by

1 paper in Pith

Heat kernel geometry and Gromov's volume growth conjecture

Receipt and verification

First computed	2026-05-18T04:08:02.765055Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1969b55599335f3e45566590887f8b90ddee828b6cbaf31e69f8638dbd05935

Aliases

arxiv: 1111.4715 · arxiv_version: 1111.4715v1 · doi: 10.48550/arxiv.1111.4715 · pith_short_12: 2GLJWVKZSM27 · pith_short_16: 2GLJWVKZSM27HZCV · pith_short_8: 2GLJWVKZ

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/2GLJWVKZSM27HZCVMZMQRB7YXE \
  | 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: d1969b55599335f3e45566590887f8b90ddee828b6cbaf31e69f8638dbd05935

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "98f61f3cd16b61a80b6d4f6514ff75065e8e8b34f7bc118f126ce72fa7bccc2b",
    "cross_cats_sorted": [
      "math.AP",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-11-21T02:16:21Z",
    "title_canon_sha256": "323e3275d3bfb40ae39423aa7a22d03174c3ca8c3ad5562668f557b5a7b0326c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.4715",
    "kind": "arxiv",
    "version": 1
  }
}