Pith Number

pith:PK72UGNJ

pith:2016:PK72UGNJFOGE4O7AEP5VQB6O4E

not attested not anchored not stored refs pending

The critical height is a moduli height

Patrick Ingram

arxiv:1610.07904 v3 · 2016-10-25 · math.NT · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PK72UGNJFOGE4O7AEP5VQB6O4E}

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	2026-05-18T00:32:51.152227Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7abfaa19a92b8c4e3be023fb5807cee125041b7d3285e809285ab97bc7570927

Aliases

arxiv: 1610.07904 · arxiv_version: 1610.07904v3 · doi: 10.48550/arxiv.1610.07904 · pith_short_12: PK72UGNJFOGE · pith_short_16: PK72UGNJFOGE4O7A · pith_short_8: PK72UGNJ

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/PK72UGNJFOGE4O7AEP5VQB6O4E \
  | 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: 7abfaa19a92b8c4e3be023fb5807cee125041b7d3285e809285ab97bc7570927

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "50042c8f17bae41b808a0bb4d1d04ad62d4e35b5c2e898a39e15d836cc30faf8",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-10-25T14:54:25Z",
    "title_canon_sha256": "1120065f0c85f14390e22cc405d208dbc93846f07d654947b46fd73b017273b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.07904",
    "kind": "arxiv",
    "version": 3
  }
}