Pith Number

pith:YXLAC5CM

pith:2019:YXLAC5CMADEQS24ETDT455WOSR

not attested not anchored not stored refs pending

Homotopies in Grothendieck fibrations

Joseph Helfer

arxiv:1905.10690 v3 · 2019-05-25 · math.CT · 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{YXLAC5CMADEQS24ETDT455WOSR}

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.

Cited by

1 paper in Pith

First-order homotopical logic

Receipt and verification

First computed	2026-07-05T03:59:19.918015Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c5d601744c00c9096b8498e7cef6ce945d262ecf3dbe1fc758edb327e80eac7d

Aliases

arxiv: 1905.10690 · arxiv_version: 1905.10690v3 · doi: 10.48550/arxiv.1905.10690 · pith_short_12: YXLAC5CMADEQ · pith_short_16: YXLAC5CMADEQS24E · pith_short_8: YXLAC5CM

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/YXLAC5CMADEQS24ETDT455WOSR \
  | 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: c5d601744c00c9096b8498e7cef6ce945d262ecf3dbe1fc758edb327e80eac7d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "836dcb7ed61b265e5a625de0fc4059ddacc4e85d8252c7062bee1506e7cc0a95",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2019-05-25T23:05:37Z",
    "title_canon_sha256": "d8b9800875a0eb36deb76aa210736f1ff4b31e03ad0a4a6ce3034a410391387f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.10690",
    "kind": "arxiv",
    "version": 3
  }
}