Pith Number

pith:X3LE7C6X

pith:2005:X3LE7C6XIUMCXIG2MPHYJY4RZP

not attested not anchored not stored refs pending

Growth conditions and inverse producing extensions

Catalin Badea, Vladimir M\"uller

arxiv:math/0512321 v1 · 2005-12-14 · math.FA · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X3LE7C6XIUMCXIG2MPHYJY4RZP}

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	2026-05-18T00:14:16.948565Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bed64f8bd745182ba0da63cf84e391cbd9b748afb263f04310cae02d81e3a59f

Aliases

arxiv: math/0512321 · arxiv_version: math/0512321v1 · doi: 10.48550/arxiv.math/0512321 · pith_short_12: X3LE7C6XIUMC · pith_short_16: X3LE7C6XIUMCXIG2 · pith_short_8: X3LE7C6X

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/X3LE7C6XIUMCXIG2MPHYJY4RZP \
  | 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: bed64f8bd745182ba0da63cf84e391cbd9b748afb263f04310cae02d81e3a59f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d29c10525eb9466d6037c383a16512ba0e87b310fdfaf9568a513a9c78498666",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "2005-12-14T10:31:03Z",
    "title_canon_sha256": "5887a82a7a347f6f4d6d30961c19531c48cbe7d6655cbc723a2583be62b981a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0512321",
    "kind": "arxiv",
    "version": 1
  }
}