Pith Number

pith:AVAWVHQE

pith:2016:AVAWVHQETVJJBNBIFZAEA7WXCJ

not attested not anchored not stored refs pending

Characterization of projective spaces and $\mathbb P^r$-bundles as ample divisors

Jie Liu

arxiv:1611.05823 v3 · 2016-11-17 · 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{AVAWVHQETVJJBNBIFZAEA7WXCJ}

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	2026-05-18T00:33:06.954391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

05416a9e049d5290b4282e40407ed71252792b3921193914c9b186f709a0ba45

Aliases

arxiv: 1611.05823 · arxiv_version: 1611.05823v3 · doi: 10.48550/arxiv.1611.05823 · pith_short_12: AVAWVHQETVJJ · pith_short_16: AVAWVHQETVJJBNBI · pith_short_8: AVAWVHQE

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/AVAWVHQETVJJBNBIFZAEA7WXCJ \
  | 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: 05416a9e049d5290b4282e40407ed71252792b3921193914c9b186f709a0ba45

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "944534709fc0380b81fe0c8f96c0748d0eb9f23457f5788f4ed577f7c73c2214",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2016-11-17T19:18:16Z",
    "title_canon_sha256": "bcccb1de2870e4966d97322c8a2ab0d25633d8a792396453b7bcadb9cce4908e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.05823",
    "kind": "arxiv",
    "version": 3
  }
}