Pith Number

pith:AKA3RJF4

pith:2011:AKA3RJF47YASXWPJHACPRS36PI

not attested not anchored not stored refs pending

The Takagi Function and Its Properties

Jeffrey C. Lagarias

arxiv:1112.4205 v2 · 2011-12-19 · math.CA · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AKA3RJF47YASXWPJHACPRS36PI}

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	2026-05-18T03:27:32.996048Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0281b8a4bcfe012bd9e93804f8cb7e7a188a5eeab7b6409afd6ff761a47a49a3

Aliases

arxiv: 1112.4205 · arxiv_version: 1112.4205v2 · doi: 10.48550/arxiv.1112.4205 · pith_short_12: AKA3RJF47YAS · pith_short_16: AKA3RJF47YASXWPJ · pith_short_8: AKA3RJF4

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/AKA3RJF47YASXWPJHACPRS36PI \
  | 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: 0281b8a4bcfe012bd9e93804f8cb7e7a188a5eeab7b6409afd6ff761a47a49a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95cfb412fb3a4e734ecd583cd389b14606f820b07fa6bcc0245d1e6616fed995",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-12-19T00:03:49Z",
    "title_canon_sha256": "df8ad1c5a6626195008be96b3b3bdf5870e20331dadfe129f97f0dc09c59f674"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4205",
    "kind": "arxiv",
    "version": 2
  }
}