Pith Number

pith:IPLW6VRW

pith:2019:IPLW6VRW3UOK5ZTXNTSJW323YV

not attested not anchored not stored refs pending

Generalized Lens Categories via functors $\mathcal{C}^{\rm op}\to\mathsf{Cat}$

David I. Spivak

arxiv:1908.02202 v4 · 2019-08-06 · math.CT · cs.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{IPLW6VRW3UOK5ZTXNTSJW323YV}

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

Compositionality of Lyapunov functions via assume-guarantee reasoning

Receipt and verification

First computed	2026-07-05T04:05:55.454860Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

43d76f5636dd1caee6776ce49b6f5bc57c9972b4ce8f168484f540636748c284

Aliases

arxiv: 1908.02202 · arxiv_version: 1908.02202v4 · doi: 10.48550/arxiv.1908.02202 · pith_short_12: IPLW6VRW3UOK · pith_short_16: IPLW6VRW3UOK5ZTX · pith_short_8: IPLW6VRW

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/IPLW6VRW3UOK5ZTXNTSJW323YV \
  | 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: 43d76f5636dd1caee6776ce49b6f5bc57c9972b4ce8f168484f540636748c284

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c5375325e6d8543443165104058a66122b42108c2d8a58efcb41f2588e8ac780",
    "cross_cats_sorted": [
      "cs.LO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2019-08-06T15:10:42Z",
    "title_canon_sha256": "9db1dbd20d9973651bbb30a442ff093525f72d18d065785c3c7c5ddf2e58e4f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.02202",
    "kind": "arxiv",
    "version": 4
  }
}