Pith Number

pith:Q7FHXXF4

pith:2009:Q7FHXXF4EY6HBDQR5Y7X6EU4OS

not attested not anchored not stored refs pending

Flat forms, bi-Lipschitz parametrizations, and smoothability of manifolds

Juha Heinonen, Stephen Keith

arxiv:0909.3201 v3 · 2009-09-17 · math.MG · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q7FHXXF4EY6HBDQR5Y7X6EU4OS}

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	2026-05-18T04:26:45.883154Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87ca7bdcbc263c708e11ee3f7f129c7484a05182a1f0296b4c86981bcf64825d

Aliases

arxiv: 0909.3201 · arxiv_version: 0909.3201v3 · doi: 10.48550/arxiv.0909.3201 · pith_short_12: Q7FHXXF4EY6H · pith_short_16: Q7FHXXF4EY6HBDQR · pith_short_8: Q7FHXXF4

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/Q7FHXXF4EY6HBDQR5Y7X6EU4OS \
  | 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: 87ca7bdcbc263c708e11ee3f7f129c7484a05182a1f0296b4c86981bcf64825d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c69ac76a553631a36e95565184502998bbc5b5cc27e6ad9be21cc4a66782083",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2009-09-17T12:30:04Z",
    "title_canon_sha256": "9e6d34d37461f2c3e82159e96d671af6c3cb71ae8fae0eadde942536061a0c81"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.3201",
    "kind": "arxiv",
    "version": 3
  }
}