Pith Number

pith:QRWOMWVM

pith:2019:QRWOMWVMG6N7APVMSH5MXSFWCR

not attested not anchored not stored refs pending

Denseness conditions, morphisms and equivalences of toposes

Olivia Caramello

arxiv:1906.08737 v3 · 2019-06-20 · math.CT · 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{QRWOMWVMG6N7APVMSH5MXSFWCR}

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

2 papers in Pith

Duality theory for categorical theories

De Morgan's law in toposes I

Receipt and verification

First computed	2026-07-05T01:23:54.220970Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

846ce65aac379bf03eac91facbc8b614473b175f29dacbf6f4a091b3d6861501

Aliases

arxiv: 1906.08737 · arxiv_version: 1906.08737v3 · doi: 10.48550/arxiv.1906.08737 · pith_short_12: QRWOMWVMG6N7 · pith_short_16: QRWOMWVMG6N7APVM · pith_short_8: QRWOMWVM

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/QRWOMWVMG6N7APVMSH5MXSFWCR \
  | 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: 846ce65aac379bf03eac91facbc8b614473b175f29dacbf6f4a091b3d6861501

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f28ffe5e1aadeee316040be50c324ab736210a3a72ef8adf599c91c18796a17",
    "cross_cats_sorted": [
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2019-06-20T16:33:47Z",
    "title_canon_sha256": "f1df4ad3d8ad0557407562fbf875f7d73f565d8c4c9697eba17bd0229e0907d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.08737",
    "kind": "arxiv",
    "version": 3
  }
}