Pith Number

pith:COCUZZ3W

pith:2012:COCUZZ3WXLJVHP7QHAI36UOUBW

not attested not anchored not stored refs pending

The Takagi problem on the disk and bidisk

Jim Agler, John E. McCarthy, Joseph A. Ball

arxiv:1208.2704 v1 · 2012-08-13 · math.FA · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{COCUZZ3WXLJVHP7QHAI36UOUBW}

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	2026-05-18T03:48:47.586708Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13854ce776bad353bff03811bf51d40da4866bb7e84706f196ddcf024366c8c3

Aliases

arxiv: 1208.2704 · arxiv_version: 1208.2704v1 · doi: 10.48550/arxiv.1208.2704 · pith_short_12: COCUZZ3WXLJV · pith_short_16: COCUZZ3WXLJVHP7Q · pith_short_8: COCUZZ3W

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/COCUZZ3WXLJVHP7QHAI36UOUBW \
  | 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: 13854ce776bad353bff03811bf51d40da4866bb7e84706f196ddcf024366c8c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac320f2192a48d8d7676d48a19c39bd9009dacbed641dd703ad146fc31ea33d9",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-08-13T20:29:55Z",
    "title_canon_sha256": "a056a06f7b7633a5bd38aa0c35f5f357d505d41c2731678e5675cd7c937aec46"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.2704",
    "kind": "arxiv",
    "version": 1
  }
}