Pith Number

pith:GCQTTUQX

pith:2025:GCQTTUQXUSTNDVEIQIPGILM6IF

not attested not anchored not stored refs pending

A combinatorial characterization of Kim's lemma for pairs of bi-invariant types

James E. Hanson

arxiv:2507.21366 v1 · 2025-07-28 · 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{GCQTTUQXUSTNDVEIQIPGILM6IF}

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	2026-07-05T11:44:58.445355Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30a139d217a4a6d1d488821e642d9e415117048dda418548858cbcae30acc3c8

Aliases

arxiv: 2507.21366 · arxiv_version: 2507.21366v1 · doi: 10.48550/arxiv.2507.21366 · pith_short_12: GCQTTUQXUSTN · pith_short_16: GCQTTUQXUSTNDVEI · pith_short_8: GCQTTUQX

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/GCQTTUQXUSTNDVEIQIPGILM6IF \
  | 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: 30a139d217a4a6d1d488821e642d9e415117048dda418548858cbcae30acc3c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "921024d821322d1622853fdf0b172a9ad59192063d0614b4a5580ae135ff8d77",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2025-07-28T22:24:56Z",
    "title_canon_sha256": "617939bc0087d994111fb811af2b9f4050ab5ab2a278c9ecbb4769879b0efeae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.21366",
    "kind": "arxiv",
    "version": 1
  }
}