Pith Number

pith:5VPRXBBK

pith:2010:5VPRXBBKZMY2KBL66O5U64QJ5D

not attested not anchored not stored refs pending

One-dimensional Gromov minimal filling

A.A.Tuzhilin, A.O.Ivanov

arxiv:1101.0106 v2 · 2010-12-30 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5VPRXBBKZMY2KBL66O5U64QJ5D}

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	2026-05-18T02:23:05.964713Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed5f1b842acb31a5057ef3bb4f7209e8f5f1b1a058b8b7390f998a73d0fa7e9a

Aliases

arxiv: 1101.0106 · arxiv_version: 1101.0106v2 · doi: 10.48550/arxiv.1101.0106 · pith_short_12: 5VPRXBBKZMY2 · pith_short_16: 5VPRXBBKZMY2KBL6 · pith_short_8: 5VPRXBBK

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/5VPRXBBKZMY2KBL66O5U64QJ5D \
  | 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: ed5f1b842acb31a5057ef3bb4f7209e8f5f1b1a058b8b7390f998a73d0fa7e9a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "511d2863c302a43013fff2c12b7db921ab18f823fd56a36c9e059115b72d1fd3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2010-12-30T16:27:42Z",
    "title_canon_sha256": "63248fe298c7fb5526cb66337643c3edea8581797e4fbfd6488c3a62e737f47c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.0106",
    "kind": "arxiv",
    "version": 2
  }
}