Pith Number

pith:5VGS22IB

pith:2025:5VGS22IBYUPDL6YXD4XUJOEH4U

not attested not anchored not stored refs pending

Formalization of the zigzag construction of path spaces of pushouts in homotopy type theory

Vojt\v{e}ch \v{S}t\v{e}pan\v{c}\'ik

arxiv:2510.08452 v2 · 2025-10-09 · math.LO · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5VGS22IBYUPDL6YXD4XUJOEH4U}

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	2026-07-03T01:17:53.833765Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed4d2d6901c51e35fb171f2f44b887e52184ad1fc9fef4fad0498406411bf295

Aliases

arxiv: 2510.08452 · arxiv_version: 2510.08452v2 · doi: 10.48550/arxiv.2510.08452 · pith_short_12: 5VGS22IBYUPD · pith_short_16: 5VGS22IBYUPDL6YX · pith_short_8: 5VGS22IB

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/5VGS22IBYUPDL6YXD4XUJOEH4U \
  | 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: ed4d2d6901c51e35fb171f2f44b887e52184ad1fc9fef4fad0498406411bf295

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7d1a872c4dcafc7cb85473e5b2f7352ab7cb8d4c867adf72e7405f5ee1b17a7d",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2025-10-09T16:59:49Z",
    "title_canon_sha256": "d672910e24135192981595b7970aab61ffb4e450b64050b6f1cdc3f69c86c71b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.08452",
    "kind": "arxiv",
    "version": 2
  }
}