Pith Number

pith:K4F4VGGB

pith:2018:K4F4VGGBBL3GPM5GKU2IP3I7XW

not attested not anchored not stored refs pending

Categorical duality between joins and intersections

Naichung Conan Leung, Qingyuan Jiang

arxiv:1811.05135 v1 · 2018-11-13 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K4F4VGGBBL3GPM5GKU2IP3I7XW}

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	2026-05-18T00:00:46.808548Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

570bca98c10af667b3a6553487ed1fbd804b244b524c55bf430762074ef485fa

Aliases

arxiv: 1811.05135 · arxiv_version: 1811.05135v1 · doi: 10.48550/arxiv.1811.05135 · pith_short_12: K4F4VGGBBL3G · pith_short_16: K4F4VGGBBL3GPM5G · pith_short_8: K4F4VGGB

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/K4F4VGGBBL3GPM5GKU2IP3I7XW \
  | 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: 570bca98c10af667b3a6553487ed1fbd804b244b524c55bf430762074ef485fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e6262eb3c711a69b100fbe1eb469d7f16bad3e4e78b922a4720e8b8203689c7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2018-11-13T07:26:10Z",
    "title_canon_sha256": "7f98966f943d9aff02be7ef6b67927dc0bc54664c8ac2084e391e88e6bef82a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.05135",
    "kind": "arxiv",
    "version": 1
  }
}