Pith Number

pith:UXAAMBZ6

pith:2025:UXAAMBZ6A52ZWUTWUQIQNU7KSM

not attested not anchored not stored refs pending

Computation by infinite descent made explicit

Sebastian Enqvist

Every valid proof in this ordinal-annotated non-wellfounded system is computable.

arxiv:2506.22206 v6 · 2025-06-27 · cs.LO

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UXAAMBZ6A52ZWUTWUQIQNU7KSM}

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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

Every valid proof in the system is computable; as a consequence, every proof of a sequent of the appropriate form represents a unique function on natural numbers for finitary formulas.

C2weakest assumption

The definition of computability for proofs in the non-wellfounded system with ordinal annotations is sufficient to capture the computational content without additional restrictions on the ordinal variables or the interaction between inductive and co-inductive rules.

C3one line summary

Presents an ordinal-annotated non-wellfounded proof system for intuitionistic logic with fixpoints, establishes computability and normalization results for finitary formulas, and derives a categorical semantics with algebras and coalgebras.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-23T03:13:46.016634Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a5c006073e07759b5276a41106d3ea93342a762c7a2c4142df52e3dba059dc1b

Aliases

arxiv: 2506.22206 · arxiv_version: 2506.22206v6 · doi: 10.48550/arxiv.2506.22206 · pith_short_12: UXAAMBZ6A52Z · pith_short_16: UXAAMBZ6A52ZWUTW · pith_short_8: UXAAMBZ6

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/UXAAMBZ6A52ZWUTWUQIQNU7KSM \
  | 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: a5c006073e07759b5276a41106d3ea93342a762c7a2c4142df52e3dba059dc1b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95baa29bd02445a985d65f05fb15848aa9fbe55ab75a34ee3272bae435d80892",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2025-06-27T13:25:04Z",
    "title_canon_sha256": "65f6e34ae258752c2eaf94def43baeb028b5e425dd880edcf88a604fdcd9ab14"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.22206",
    "kind": "arxiv",
    "version": 6
  }
}