Pith Number

pith:CCXAIO76

pith:2008:CCXAIO76DNFPQOH3NIBQKFMNS7

not attested not anchored not stored refs pending

Complex manifolds with generating tangent bundles

Renyi Ma

arxiv:0808.2690 v4 · 2008-08-20 · math.AG · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CCXAIO76DNFPQOH3NIBQKFMNS7}

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	2026-05-18T04:00:02.926149Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

10ae043bfe1b4af838fb6a0305158d97f28129259cf7c2f0f7d13166efccd733

Aliases

arxiv: 0808.2690 · arxiv_version: 0808.2690v4 · doi: 10.48550/arxiv.0808.2690 · pith_short_12: CCXAIO76DNFP · pith_short_16: CCXAIO76DNFPQOH3 · pith_short_8: CCXAIO76

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/CCXAIO76DNFPQOH3NIBQKFMNS7 \
  | 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: 10ae043bfe1b4af838fb6a0305158d97f28129259cf7c2f0f7d13166efccd733

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "adad61a770f0fd4f83a4f2a1a4e61844a4c7f4892ecaa499e680d7d555db0509",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2008-08-20T04:21:05Z",
    "title_canon_sha256": "169f46fba7a67a67eed3ef8f1d810d5400d1e43b3687d5e81fa1b0663d59ead8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0808.2690",
    "kind": "arxiv",
    "version": 4
  }
}