Pith Number

pith:43G77UWR

pith:2026:43G77UWRMLZCVKT7LLLHJK76W7

not attested not anchored not stored refs resolved

What can Topology tell us about Logical Complexity?

Ming Ng, Takayuki Kihara

A computable variant of the gamified Katětov order on filters is isomorphic to the Lawvere-Tierney order, linking combinatorial complexity measures to computability in topos theory.

arxiv:2605.14086 v1 · 2026-05-13 · math.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{43G77UWRMLZCVKT7LLLHJK76W7}

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.

Claims

C1strongest claim

a computable variant of the gamified Katětov order is isomorphic to the original ≤_LT-order

C2weakest assumption

That the gamified Katětov order, closed under well-founded iterations of Fubini powers, precisely captures the combinatorial complexity shifts already present in the Lawvere-Tierney order.

C3one line summary

A computable variant of the gamified Katětov order on filters is isomorphic to the Lawvere-Tierney order, linking combinatorial complexity measures to computability in topos theory.

References

145 extracted · 145 resolved · 0 Pith anchors

[1] Orderings of ultrafilters , year =

[2] Partial orders on the types in N , url = 1971

[3] Takayuki Kihara and Ming Ng , date-added =. The

[4] Filip. On. 2013 , bdsk-url-1 =. doi:10.1016/j.topol.2013.08.007 , journal = 2013 · doi:10.1016/j.topol.2013.08.007

[5] A UNIFIED APPROACH TO 2024 · doi:10.1017/jsl.2024.8

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:12.261971Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6cdffd2d162f22aaa7f5ad674abfeb7ed6e767e4c6d46746cf5af0ad6686dd0

Aliases

arxiv: 2605.14086 · arxiv_version: 2605.14086v1 · doi: 10.48550/arxiv.2605.14086 · pith_short_12: 43G77UWRMLZC · pith_short_16: 43G77UWRMLZCVKT7 · pith_short_8: 43G77UWR

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/43G77UWRMLZCVKT7LLLHJK76W7 \
  | 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: e6cdffd2d162f22aaa7f5ad674abfeb7ed6e767e4c6d46746cf5af0ad6686dd0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d6fa0990901aa13245bc27e6d133fb55d79b9833a80bdd6473762834ee0dc2b",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2026-05-13T20:12:08Z",
    "title_canon_sha256": "96d9641c5a1dfb4656ac51f110b42f2768f8d755c8caadc14a3b42f99878fee1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14086",
    "kind": "arxiv",
    "version": 1
  }
}