Pith Number

pith:FBTPLIIM

pith:2012:FBTPLIIMLZ7CNZN75K5UCNESA3

not attested not anchored not stored refs pending

On the Local $Tb$ Theorem: A Direct Proof under Duality Assumption

Antti V. V\"ah\"akangas, Michael T. Lacey

arxiv:1209.4161 v2 · 2012-09-19 · 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{FBTPLIIMLZ7CNZN75K5UCNESA3}

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	2026-05-18T01:16:01.214565Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2866f5a10c5e7e26e5bfeabb41349206cd7db4b56d6c6d4b26bdd5074293e090

Aliases

arxiv: 1209.4161 · arxiv_version: 1209.4161v2 · doi: 10.48550/arxiv.1209.4161 · pith_short_12: FBTPLIIMLZ7C · pith_short_16: FBTPLIIMLZ7CNZN7 · pith_short_8: FBTPLIIM

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/FBTPLIIMLZ7CNZN75K5UCNESA3 \
  | 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: 2866f5a10c5e7e26e5bfeabb41349206cd7db4b56d6c6d4b26bdd5074293e090

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7d6e3aa1cc0609d3a77c56fcad5973a7554ee01fcae482ba65e74049495ba034",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-09-19T06:52:09Z",
    "title_canon_sha256": "3ce3bb1b8eb745221c64b18ecb44d42a7e878825d9cd76406b8daf782d0332c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.4161",
    "kind": "arxiv",
    "version": 2
  }
}