Pith Number

pith:XQQKDKZ7

pith:2026:XQQKDKZ7HMNMA4G66RXBHHJIH4

not attested not anchored not stored refs pending

The Leibniz adjunction in homotopy type theory, with an application to simplicial type theory

Axel Ljungstr\"om, Nicolai Kraus, Tom de Jong

arxiv:2601.21843 v2 · 2026-01-29 · math.CT · cs.LO · 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{XQQKDKZ7HMNMA4G66RXBHHJIH4}

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	2026-06-19T16:11:20.070145Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc20a1ab3f3b1ac070def46e139d283f2746b8ad5e83ca039d374eeed0fbff5a

Aliases

arxiv: 2601.21843 · arxiv_version: 2601.21843v2 · doi: 10.48550/arxiv.2601.21843 · pith_short_12: XQQKDKZ7HMNM · pith_short_16: XQQKDKZ7HMNMA4G6 · pith_short_8: XQQKDKZ7

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/XQQKDKZ7HMNMA4G66RXBHHJIH4 \
  | 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: bc20a1ab3f3b1ac070def46e139d283f2746b8ad5e83ca039d374eeed0fbff5a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6af07d4866afc79ab9a8f20e463cd4973c3935ebae535ad5e6addd132583352",
    "cross_cats_sorted": [
      "cs.LO",
      "math.LO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2026-01-29T15:19:28Z",
    "title_canon_sha256": "4e653f76b6c20ddf7297165f6d533b9f1504027cfba77aebbc96baeefd4f8b7c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.21843",
    "kind": "arxiv",
    "version": 2
  }
}