Pith Number

pith:4CXAQO62

pith:2019:4CXAQO62KXI5PFGYM3TUSS3QT6

not attested not anchored not stored refs pending

Covariant & Contravariant Homotopy Theories

Hoang Kim Nguyen

arxiv:1908.06879 v1 · 2019-08-19 · 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{4CXAQO62KXI5PFGYM3TUSS3QT6}

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	2026-07-04T23:58:20.630756Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0ae083bda55d1d794d866e7494b709fbc67306f6f01b9d18579f021de48013d

Aliases

arxiv: 1908.06879 · arxiv_version: 1908.06879v1 · doi: 10.48550/arxiv.1908.06879 · pith_short_12: 4CXAQO62KXI5 · pith_short_16: 4CXAQO62KXI5PFGY · pith_short_8: 4CXAQO62

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/4CXAQO62KXI5PFGYM3TUSS3QT6 \
  | 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: e0ae083bda55d1d794d866e7494b709fbc67306f6f01b9d18579f021de48013d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4b90d60b93ba56b7e7c9d0f3681da52b30e3c045762a95745c29447cbafecbc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2019-08-19T15:31:58Z",
    "title_canon_sha256": "1b0769e484bc22420e6d71f40c177abcf6912429b60323a79de9a2bdda6dc4a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.06879",
    "kind": "arxiv",
    "version": 1
  }
}