Pith Number

pith:MLANMMI2

pith:2012:MLANMMI2ZPW4LMUG35T6V7MTI7

not attested not anchored not stored refs pending

Ricci curvature and monotonicity for harmonic functions

Tobias Holck Colding, William P. Minicozzi II

arxiv:1209.4669 v1 · 2012-09-20 · 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{MLANMMI2ZPW4LMUG35T6V7MTI7}

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	2026-05-18T03:45:10.313931Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62c0d6311acbedc5b286df67eafd9347e080b432c687519bde1eda65f278c76a

Aliases

arxiv: 1209.4669 · arxiv_version: 1209.4669v1 · doi: 10.48550/arxiv.1209.4669 · pith_short_12: MLANMMI2ZPW4 · pith_short_16: MLANMMI2ZPW4LMUG · pith_short_8: MLANMMI2

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/MLANMMI2ZPW4LMUG35T6V7MTI7 \
  | 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: 62c0d6311acbedc5b286df67eafd9347e080b432c687519bde1eda65f278c76a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47e8cd0b4833c940f79d7570d79af1de184e00f925abced1ab34d553f608cee9",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-09-20T21:12:02Z",
    "title_canon_sha256": "1aca147bb38a183051196b45c595135893355194386cbb65e56201b8a0b96373"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.4669",
    "kind": "arxiv",
    "version": 1
  }
}