Pith Number

pith:RBDAO6GQ

pith:2023:RBDAO6GQBKLFKNDRCVLLAR2MSA

not attested not anchored not stored refs pending

Positivity of exterior products of tangent bundles and their subsheaves

Yuting Liu

arxiv:2310.19315 v3 · 2023-10-30 · 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{RBDAO6GQBKLFKNDRCVLLAR2MSA}

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	2026-07-05T07:28:31.016624Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

88460778d00a965534711556b0474c901f2702475ae8e8af1696241905716a86

Aliases

arxiv: 2310.19315 · arxiv_version: 2310.19315v3 · doi: 10.48550/arxiv.2310.19315 · pith_short_12: RBDAO6GQBKLF · pith_short_16: RBDAO6GQBKLFKNDR · pith_short_8: RBDAO6GQ

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/RBDAO6GQBKLFKNDRCVLLAR2MSA \
  | 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: 88460778d00a965534711556b0474c901f2702475ae8e8af1696241905716a86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b57e73828946b327c6a04de049bea2941596ed00fbc5392a54412f05f5662cba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2023-10-30T07:24:52Z",
    "title_canon_sha256": "8ad7a6e518177e0b7a449064eb469c6a764a82ed7f10de9b3e5fb8d025ea3a68"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2310.19315",
    "kind": "arxiv",
    "version": 3
  }
}