Pith Number

pith:WGCB4PC7

pith:2012:WGCB4PC7DYXTQDROGOOYS26QWK

not attested not anchored not stored refs pending

Monotonicity - analytic and geometric implications

Tobias Holck Colding, William P. Minicozzi II

arxiv:1205.6768 v2 · 2012-05-30 · 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{WGCB4PC7DYXTQDROGOOYS26QWK}

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	2026-05-18T03:54:03.900063Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1841e3c5f1e2f380e2e339d896bd0b2a4aa034d4b3e7f0e64865c9cad4c5e51

Aliases

arxiv: 1205.6768 · arxiv_version: 1205.6768v2 · doi: 10.48550/arxiv.1205.6768 · pith_short_12: WGCB4PC7DYXT · pith_short_16: WGCB4PC7DYXTQDRO · pith_short_8: WGCB4PC7

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/WGCB4PC7DYXTQDROGOOYS26QWK \
  | 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: b1841e3c5f1e2f380e2e339d896bd0b2a4aa034d4b3e7f0e64865c9cad4c5e51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0a9eedbd6f54d793acfdfc5b58df332a1bf543a9995a74630c2e2a0f3b3484b",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-05-30T17:45:56Z",
    "title_canon_sha256": "7884fda140dbcc3972d7e13a312101e73b05e98e151a9c58b1d966e563d79963"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.6768",
    "kind": "arxiv",
    "version": 2
  }
}