Pith Number

pith:ZE7DL46F

pith:2011:ZE7DL46FIX6FYF6DT3B3MGWOPB

not attested not anchored not stored refs pending

Lefschetz properties and the Veronese construction

Martina Kubitzke, Satoshi Murai

arxiv:1112.5015 v1 · 2011-12-21 · math.CO · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZE7DL46FIX6FYF6DT3B3MGWOPB}

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	2026-05-18T04:05:56.461067Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c93e35f3c545fc5c17c39ec3b61ace7849f118bc7f7994cb94b9c1fd5ec5abf2

Aliases

arxiv: 1112.5015 · arxiv_version: 1112.5015v1 · doi: 10.48550/arxiv.1112.5015 · pith_short_12: ZE7DL46FIX6F · pith_short_16: ZE7DL46FIX6FYF6D · pith_short_8: ZE7DL46F

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/ZE7DL46FIX6FYF6DT3B3MGWOPB \
  | 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: c93e35f3c545fc5c17c39ec3b61ace7849f118bc7f7994cb94b9c1fd5ec5abf2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5307992e4c87ff6982c37b338b9d595ae5ead695a67dc30228ce6a4aa5887fc4",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-12-21T13:17:51Z",
    "title_canon_sha256": "71dec347ba3ae0f085c9552a4c536c3efd261757ca957de22fb556876e6fd0b5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.5015",
    "kind": "arxiv",
    "version": 1
  }
}