Pith Number

pith:ZBNS7G5V

pith:1997:ZBNS7G5VSQBROZQGN4CYEI44GC

not attested not anchored not stored refs pending

The condition in the Trichotomy Theorem is optimal

Menachem Kojman, Saharon Shelah

arxiv:math/9712289 v1 · 1997-12-15 · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZBNS7G5VSQBROZQGN4CYEI44GC}

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	2026-05-18T01:05:34.468760Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c85b2f9bb594031766066f0582239c309c9883f698984b2c46d8adc9c2e50c12

Aliases

arxiv: math/9712289 · arxiv_version: math/9712289v1 · doi: 10.48550/arxiv.math/9712289 · pith_short_12: ZBNS7G5VSQBR · pith_short_16: ZBNS7G5VSQBROZQG · pith_short_8: ZBNS7G5V

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/ZBNS7G5VSQBROZQGN4CYEI44GC \
  | 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: c85b2f9bb594031766066f0582239c309c9883f698984b2c46d8adc9c2e50c12

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86063c23db56e12b2dcada488d136744a8897fe94913cfe8eca5f2316deb32c8",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.LO",
    "submitted_at": "1997-12-15T00:00:00Z",
    "title_canon_sha256": "c273d1a20b9d38f6ba6712dfdbe55b18987b03c0340c7818eba27a93cd762876"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9712289",
    "kind": "arxiv",
    "version": 1
  }
}