Pith Number

pith:IPTPXKXX

pith:2011:IPTPXKXXJARZG5ZK7QF5GHGLLB

not attested not anchored not stored refs pending

The Takagi function: a survey

Kiko Kawamura, Pieter Allaart

arxiv:1110.1691 v2 · 2011-10-08 · 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{IPTPXKXXJARZG5ZK7QF5GHGLLB}

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	2026-05-18T03:48:48.093347Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

43e6fbaaf7482393772afc0bd31ccb5866797619ba662b3282a70c9b0b396cc4

Aliases

arxiv: 1110.1691 · arxiv_version: 1110.1691v2 · doi: 10.48550/arxiv.1110.1691 · pith_short_12: IPTPXKXXJARZ · pith_short_16: IPTPXKXXJARZG5ZK · pith_short_8: IPTPXKXX

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/IPTPXKXXJARZG5ZK7QF5GHGLLB \
  | 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: 43e6fbaaf7482393772afc0bd31ccb5866797619ba662b3282a70c9b0b396cc4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "65d227c2e78e24a95f7d6bf3f793b3ab74abcca275f733038ca25fe956e82f65",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-10-08T03:49:37Z",
    "title_canon_sha256": "a255e8c24511d29871c0a3c68881cb1f3606088db4d4b6550b1a5e0abdb0534f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.1691",
    "kind": "arxiv",
    "version": 2
  }
}