Pith Number

pith:XKP5Y536

pith:2010:XKP5Y536PC2KQX42AOUNSOLMKI

not attested not anchored not stored refs pending

Metric currents, differentiable structures, and Carnot groups

Marshall Williams

arxiv:1008.4120 v2 · 2010-08-24 · math.MG · math.DG · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XKP5Y536PC2KQX42AOUNSOLMKI}

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	2026-05-18T04:29:55.543198Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba9fdc777e78b4a85f9a03a8d9396c521e9c00a0c56e9aa1c561986539446bb7

Aliases

arxiv: 1008.4120 · arxiv_version: 1008.4120v2 · doi: 10.48550/arxiv.1008.4120 · pith_short_12: XKP5Y536PC2K · pith_short_16: XKP5Y536PC2KQX42 · pith_short_8: XKP5Y536

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/XKP5Y536PC2KQX42AOUNSOLMKI \
  | 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: ba9fdc777e78b4a85f9a03a8d9396c521e9c00a0c56e9aa1c561986539446bb7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5fc26454570ee6ce7d8dc9162932d9abf76f6c7a5bed5d47c34472166f8982b0",
    "cross_cats_sorted": [
      "math.DG",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2010-08-24T19:35:23Z",
    "title_canon_sha256": "0565548607bdac3aacd45392240511de5d5239b182e67e23e86e6f90c6acf39e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.4120",
    "kind": "arxiv",
    "version": 2
  }
}