Pith Number

pith:Z5UK64CB

pith:2015:Z5UK64CBV3T7BCKYISLHKBROWK

not attested not anchored not stored refs pending

An Isbell Duality Theorem for Type Refinement Systems

Noam Zeilberger, Paul-Andr\'e Melli\`es

arxiv:1501.05115 v2 · 2015-01-21 · cs.LO · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z5UK64CBV3T7BCKYISLHKBROWK}

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	2026-05-18T01:36:01.640400Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf68af7041aee7f08958449675062eb2918b6463d6b4908341031fc9decb7ae8

Aliases

arxiv: 1501.05115 · arxiv_version: 1501.05115v2 · doi: 10.48550/arxiv.1501.05115 · pith_short_12: Z5UK64CBV3T7 · pith_short_16: Z5UK64CBV3T7BCKY · pith_short_8: Z5UK64CB

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/Z5UK64CBV3T7BCKYISLHKBROWK \
  | 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: cf68af7041aee7f08958449675062eb2918b6463d6b4908341031fc9decb7ae8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf0797491a9594c00840d54181108a9f87bfae60c510f30c747d750e7e79d2d7",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2015-01-21T10:24:16Z",
    "title_canon_sha256": "08f7f9838385b50d459040b5986bceb4c8b2a2c851069d65b4cbff59ed916d6a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.05115",
    "kind": "arxiv",
    "version": 2
  }
}