Pith Number

pith:26I7N5OR

pith:2023:26I7N5ORSGT4ZQFYE2HIXEKSCG

not attested not anchored not stored refs pending

Lojasiewicz inequalities for maps of the 2-sphere

Alex Waldron

arxiv:2312.16686 v2 · 2023-12-27 · 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{26I7N5ORSGT4ZQFYE2HIXEKSCG}

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

Strong uniqueness and rectifiability of generalized cylindrical singularities in Ricci flow

Receipt and verification

First computed	2026-07-05T10:46:35.977626Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d791f6f5d191a7ccc0b8268e8b915211897a80beb62f6d69f84deadc6ffca0ce

Aliases

arxiv: 2312.16686 · arxiv_version: 2312.16686v2 · doi: 10.48550/arxiv.2312.16686 · pith_short_12: 26I7N5ORSGT4 · pith_short_16: 26I7N5ORSGT4ZQFY · pith_short_8: 26I7N5OR

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/26I7N5ORSGT4ZQFYE2HIXEKSCG \
  | 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: d791f6f5d191a7ccc0b8268e8b915211897a80beb62f6d69f84deadc6ffca0ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2fbdcdf62e2926828e78f509d44c6ff45993cb2f7749f0ff592da8e9db05c672",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2023-12-27T18:58:54Z",
    "title_canon_sha256": "6d2546ec30df557a9b7ae78f9cbc8e9ee0d0068fe556ea574475fe433c0904d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2312.16686",
    "kind": "arxiv",
    "version": 2
  }
}