Pith Number

pith:XAHIVGYO

pith:2011:XAHIVGYOXYBI77IHJYY3CEOO5D

not attested not anchored not stored refs pending

A quantitative metric differentiation theorem

Jonas Azzam, Raanan Schul

arxiv:1111.2561 v3 · 2011-11-10 · math.MG · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XAHIVGYOXYBI77IHJYY3CEOO5D}

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	2026-05-18T03:52:51.103641Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b80e8a9b0ebe028ffd074e31b111cee8f4ac5c6aaf35f1433c937e80a13687bf

Aliases

arxiv: 1111.2561 · arxiv_version: 1111.2561v3 · doi: 10.48550/arxiv.1111.2561 · pith_short_12: XAHIVGYOXYBI · pith_short_16: XAHIVGYOXYBI77IH · pith_short_8: XAHIVGYO

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/XAHIVGYOXYBI77IHJYY3CEOO5D \
  | 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: b80e8a9b0ebe028ffd074e31b111cee8f4ac5c6aaf35f1433c937e80a13687bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d83fe645433c3ff81b58979f5a4de4800ab7e357e3b058d26cdbcbcf9250a2d3",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2011-11-10T19:00:59Z",
    "title_canon_sha256": "e6496b14aad8bbbb295a1de5fcf066a89c5323fe4d0b2bf621431fd5799df51d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.2561",
    "kind": "arxiv",
    "version": 3
  }
}