Pith Number

pith:6YR5ITAI

pith:2013:6YR5ITAIN2FUJZUBDM62KSKS3A

not attested not anchored not stored refs pending

Uniqueness of blowups and Lojasiewicz inequalities

Tobias Holck Colding, William P. Minicozzi II

arxiv:1312.4046 v2 · 2013-12-14 · 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{6YR5ITAIN2FUJZUBDM62KSKS3A}

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	2026-05-18T02:51:33.727969Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f623d44c086e8b44e6811b3da54952d839cec9dbb8eb279fd97e0b7b0da43c4d

Aliases

arxiv: 1312.4046 · arxiv_version: 1312.4046v2 · doi: 10.48550/arxiv.1312.4046 · pith_short_12: 6YR5ITAIN2FU · pith_short_16: 6YR5ITAIN2FUJZUB · pith_short_8: 6YR5ITAI

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/6YR5ITAIN2FUJZUBDM62KSKS3A \
  | 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: f623d44c086e8b44e6811b3da54952d839cec9dbb8eb279fd97e0b7b0da43c4d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a5bb3eb02a00d3e1e93b106ab5c2534a0691402d33c7a870acd9811dd8eaf6bd",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2013-12-14T13:50:16Z",
    "title_canon_sha256": "cfd03ee41ca3fca28c6f7fd25550abfe354a22c10efc30c0186c1b5137e1c293"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.4046",
    "kind": "arxiv",
    "version": 2
  }
}