Pith Number

pith:VRHOWZM4

pith:2010:VRHOWZM4PDKQLKVQSBUT5YJO7S

not attested not anchored not stored refs pending

Metric spaces with unique tangents

Enrico Le Donne

arxiv:1012.2210 v1 · 2010-12-10 · math.MG · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VRHOWZM4PDKQLKVQSBUT5YJO7S}

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	2026-05-18T04:33:38.278747Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac4eeb659c78d505aab090693ee12efc955ab95f8fac72a120dcb5e67b6a4959

Aliases

arxiv: 1012.2210 · arxiv_version: 1012.2210v1 · doi: 10.48550/arxiv.1012.2210 · pith_short_12: VRHOWZM4PDKQ · pith_short_16: VRHOWZM4PDKQLKVQ · pith_short_8: VRHOWZM4

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/VRHOWZM4PDKQLKVQSBUT5YJO7S \
  | 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: ac4eeb659c78d505aab090693ee12efc955ab95f8fac72a120dcb5e67b6a4959

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0443a36bc4ac005853079493e398e38031e2bec54cfa505aa45ae4c0379126c1",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2010-12-10T09:09:43Z",
    "title_canon_sha256": "72df011292b7272f9f3fed37abbaccf93a69daa97318c80032472642024e09e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2210",
    "kind": "arxiv",
    "version": 1
  }
}