Pith Number

pith:2XY5VGLD

pith:2025:2XY5VGLDQYD6QQ4SXRMGKB2LX7

not attested not anchored not stored refs pending

Logical Aspects of Virtual Double Categories

Hayato Nasu

arxiv:2501.17869 v2 · 2025-01-15 · 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{2XY5VGLDQYD6QQ4SXRMGKB2LX7}

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	2026-07-05T10:07:48.628205Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d5f1da99638607e84392bc5865074bbfff8edeaa8bc7f6e4e4f90e5f1878c921

Aliases

arxiv: 2501.17869 · arxiv_version: 2501.17869v2 · doi: 10.48550/arxiv.2501.17869 · pith_short_12: 2XY5VGLDQYD6 · pith_short_16: 2XY5VGLDQYD6QQ4S · pith_short_8: 2XY5VGLD

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/2XY5VGLDQYD6QQ4SXRMGKB2LX7 \
  | 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: d5f1da99638607e84392bc5865074bbfff8edeaa8bc7f6e4e4f90e5f1878c921

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e0f5916b7a548bb18436e297d5ab5ff5c132121c3c57342809e1706614ab32da",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2025-01-15T08:42:56Z",
    "title_canon_sha256": "ac031cb4054859f0978fba57877fe8a951c5ef589f2eba72f49764f18a80e9f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.17869",
    "kind": "arxiv",
    "version": 2
  }
}