Pith Number

pith:GQ4YL7Y4

pith:2014:GQ4YL7Y4RFLDYF34VYK4FNHCKT

not attested not anchored not stored refs pending

Proportionality Principle for the Lipschitz simplicial volume

Federico Franceschini

arxiv:1411.0147 v1 · 2014-11-01 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GQ4YL7Y4RFLDYF34VYK4FNHCKT}

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	2026-05-18T02:38:52.434917Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

343985ff1c89563c177cae15c2b4e254db5ff944665ee88899aa4ee8e955f922

Aliases

arxiv: 1411.0147 · arxiv_version: 1411.0147v1 · doi: 10.48550/arxiv.1411.0147 · pith_short_12: GQ4YL7Y4RFLD · pith_short_16: GQ4YL7Y4RFLDYF34 · pith_short_8: GQ4YL7Y4

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/GQ4YL7Y4RFLDYF34VYK4FNHCKT \
  | 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: 343985ff1c89563c177cae15c2b4e254db5ff944665ee88899aa4ee8e955f922

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "506b2890ae76ec6c9221b467f29ae312340befc87134237fbd5e52c3e5d1c6c5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2014-11-01T18:24:40Z",
    "title_canon_sha256": "8431ef89d7e02b775a6aa370e4b08002a5f75faae39d442183aded078bc6677b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.0147",
    "kind": "arxiv",
    "version": 1
  }
}