Pith Number

pith:WFJQY6MR

pith:2016:WFJQY6MR6L5KZZO46G7IC6J2GB

not attested not anchored not stored refs pending

Contravariance through enrichment

Michael Shulman

arxiv:1606.05058 v2 · 2016-06-16 · 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{WFJQY6MR6L5KZZO46G7IC6J2GB}

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

Doctrinal Semantics of Directed First-Order Logic

Receipt and verification

First computed	2026-05-18T00:25:08.067281Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1530c7991f2faace5dcf1be81793a3053ce590810a990aa698f6a55867275cf

Aliases

arxiv: 1606.05058 · arxiv_version: 1606.05058v2 · doi: 10.48550/arxiv.1606.05058 · pith_short_12: WFJQY6MR6L5K · pith_short_16: WFJQY6MR6L5KZZO4 · pith_short_8: WFJQY6MR

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/WFJQY6MR6L5KZZO46G7IC6J2GB \
  | 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: b1530c7991f2faace5dcf1be81793a3053ce590810a990aa698f6a55867275cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e91cb37ce7f1cf1b35aa52634cd9336b1c99ec1b575a58e78c734b501491ec1d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2016-06-16T05:47:08Z",
    "title_canon_sha256": "cd25d28c554290098fd844fc2aa275b7cd905d21620c4d35b90e26ed3c69d578"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.05058",
    "kind": "arxiv",
    "version": 2
  }
}