Pith Number

pith:ZXKNH3EO

pith:2019:ZXKNH3EO6MXQQD7IX2BIC5LV54

not attested not anchored not stored refs pending

Entropy and codimension bounds for generic singularities

Tobias Holck Colding, William P. Minicozzi II

arxiv:1906.07609 v2 · 2019-06-18 · math.DG · math.AP · math.GT · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZXKNH3EO6MXQQD7IX2BIC5LV54}

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	2026-05-17T23:41:00.603205Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cdd4d3ec8ef32f080fe8be82817575ef169337900e79148bda48e44d2e29c3b3

Aliases

arxiv: 1906.07609 · arxiv_version: 1906.07609v2 · doi: 10.48550/arxiv.1906.07609 · pith_short_12: ZXKNH3EO6MXQ · pith_short_16: ZXKNH3EO6MXQQD7I · pith_short_8: ZXKNH3EO

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/ZXKNH3EO6MXQQD7IX2BIC5LV54 \
  | 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: cdd4d3ec8ef32f080fe8be82817575ef169337900e79148bda48e44d2e29c3b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c7fa78ce64da98d590299e7b8ddbc6e53e798f3787101312557e593cc065193d",
    "cross_cats_sorted": [
      "math.AP",
      "math.GT",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2019-06-18T14:30:58Z",
    "title_canon_sha256": "a2fde676a9517220fef21fc4733504b7a66566fec0eb43ab5af65c345c63c6c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.07609",
    "kind": "arxiv",
    "version": 2
  }
}