Pith Number

pith:IPGZYQ44

pith:2012:IPGZYQ44FKYNCDJBE6L5KX6R6B

not attested not anchored not stored refs pending

Strong Banach property (T), after Vincent Lafforgue

Benben Liao

arxiv:1212.4646 v1 · 2012-12-19 · math.OA · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IPGZYQ44FKYNCDJBE6L5KX6R6B}

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	2026-05-18T03:38:11.818487Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

43cd9c439c2ab0d10d212797d55fd1f06e51449ce8781b33cd2f5154c36ab4bd

Aliases

arxiv: 1212.4646 · arxiv_version: 1212.4646v1 · doi: 10.48550/arxiv.1212.4646 · pith_short_12: IPGZYQ44FKYN · pith_short_16: IPGZYQ44FKYNCDJB · pith_short_8: IPGZYQ44

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/IPGZYQ44FKYNCDJBE6L5KX6R6B \
  | 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: 43cd9c439c2ab0d10d212797d55fd1f06e51449ce8781b33cd2f5154c36ab4bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "658b788ad7d53307ad7179fcc27899211054b46659ffc4fef5253ff41a260dd8",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2012-12-19T13:07:11Z",
    "title_canon_sha256": "db0eac72282d21f1f1e21fec05b2c6140dfcfd7e33f3ad74818c685543fdb600"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.4646",
    "kind": "arxiv",
    "version": 1
  }
}