Pith Number

pith:VP7KSOPL

pith:2024:VP7KSOPLD6B4LRYDS7WEFPTGSC

not attested not anchored not stored refs pending

Extension of Gromov's Lipschitz order to with additive errors

Hiroki Nakajima

arxiv:2409.02459 v1 · 2024-09-04 · 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{VP7KSOPLD6B4LRYDS7WEFPTGSC}

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	2026-07-05T09:03:05.133339Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abfea939eb1f83c5c70397ec42be66908f7861c1e32e0ceda41ab640a6e14173

Aliases

arxiv: 2409.02459 · arxiv_version: 2409.02459v1 · doi: 10.48550/arxiv.2409.02459 · pith_short_12: VP7KSOPLD6B4 · pith_short_16: VP7KSOPLD6B4LRYD · pith_short_8: VP7KSOPL

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/VP7KSOPLD6B4LRYDS7WEFPTGSC \
  | 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: abfea939eb1f83c5c70397ec42be66908f7861c1e32e0ceda41ab640a6e14173

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a7cd0b9a1d7c44aca5c8f864ebd025f20bb942c6c18923fe9600fa16e2268bb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2024-09-04T05:49:12Z",
    "title_canon_sha256": "e566bc3381143f50aebd9b8191a0e513ff295740a18d45b6eccc5e6125a8b7d6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2409.02459",
    "kind": "arxiv",
    "version": 1
  }
}