Pith Number

pith:23ZGDBMJ

pith:2012:23ZGDBMJCKN5UOFOR4NEWDNH2O

not attested not anchored not stored refs pending

Singularity results for functional equations driven by linear fractional transformations

Kazuki Okamura

arxiv:1205.3632 v2 · 2012-05-16 · math.PR · 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{23ZGDBMJCKN5UOFOR4NEWDNH2O}

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	2026-05-18T01:25:56.029973Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6f2618589129bda38ae8f1a4b0da7d39b2c72482e75bf52eb3c4148b7dc52cd

Aliases

arxiv: 1205.3632 · arxiv_version: 1205.3632v2 · doi: 10.48550/arxiv.1205.3632 · pith_short_12: 23ZGDBMJCKN5 · pith_short_16: 23ZGDBMJCKN5UOFO · pith_short_8: 23ZGDBMJ

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/23ZGDBMJCKN5UOFOR4NEWDNH2O \
  | 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: d6f2618589129bda38ae8f1a4b0da7d39b2c72482e75bf52eb3c4148b7dc52cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0c05b62fb008375cdb0ff7c4e1c70dd4fc5e5e5ec8f5c423472e639c7e9fca8",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-05-16T11:08:26Z",
    "title_canon_sha256": "43243c62a2f6defd3740bc6ba2a6df1c01242d5c6cb9e56e93dbc6e8e88a7c0d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.3632",
    "kind": "arxiv",
    "version": 2
  }
}