Pith Number

pith:MLERTPFY

pith:2004:MLERTPFYCJFVFXBYY2DRZGYWIL

not attested not anchored not stored refs pending

Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms

David Mumford, Peter W. Michor

arxiv:math/0409303 v2 · 2004-09-17 · 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{MLERTPFYCJFVFXBYY2DRZGYWIL}

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	2026-05-18T01:05:25.980734Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62c919bcb8124b52dc38c6871c9b1642d238d973da465fce9941c48b86e1ac86

Aliases

arxiv: math/0409303 · arxiv_version: math/0409303v2 · doi: 10.48550/arxiv.math/0409303 · pith_short_12: MLERTPFYCJFV · pith_short_16: MLERTPFYCJFVFXBY · pith_short_8: MLERTPFY

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/MLERTPFYCJFVFXBYY2DRZGYWIL \
  | 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: 62c919bcb8124b52dc38c6871c9b1642d238d973da465fce9941c48b86e1ac86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ebaf61bb855882213999b42653a5cd88f976e148d6b8ce0ba3590cc2bc3f3189",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2004-09-17T15:16:55Z",
    "title_canon_sha256": "27a289670360e3009e45cf20b3876e73af8dcd8281ecc84eaa5a5b09cd1cde83"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0409303",
    "kind": "arxiv",
    "version": 2
  }
}