Pith Number

pith:PWZNFNZI

pith:2009:PWZNFNZI6UEN4R3K646NVZY33A

not attested not anchored not stored refs pending

The factor set of Gr-categories of the type $(\Pi,A)$

Nguyen Tien Quang

arxiv:0911.1689 v1 · 2009-11-09 · 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{PWZNFNZI6UEN4R3K646NVZY33A}

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	2026-05-18T03:37:09.488200Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7db2d2b728f508de476af73cdae71bd83ac1cf03f364d19ab70395df2d8a1a48

Aliases

arxiv: 0911.1689 · arxiv_version: 0911.1689v1 · doi: 10.48550/arxiv.0911.1689 · pith_short_12: PWZNFNZI6UEN · pith_short_16: PWZNFNZI6UEN4R3K · pith_short_8: PWZNFNZI

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/PWZNFNZI6UEN4R3K646NVZY33A \
  | 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: 7db2d2b728f508de476af73cdae71bd83ac1cf03f364d19ab70395df2d8a1a48

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "04a2bc6fdb59b03f8e49b545b84df5695fdff1280e4bb977d95e8d6bdb2fde7e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2009-11-09T14:30:12Z",
    "title_canon_sha256": "9c2ea128f3f76b99b4bbda8483ec0dd9185f46a97048d1f993925ee19c94fcce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.1689",
    "kind": "arxiv",
    "version": 1
  }
}