Pith Number

pith:2T4CQSBK

pith:2009:2T4CQSBKDAQ2KNDGOBRX34PZC3

not attested not anchored not stored refs pending

Combinatorial bounds on Hilbert functions of fat points in projective space

Brian Harbourne, Susan Cooper, Zach Teitler

arxiv:0912.1915 v3 · 2009-12-10 · math.AG · 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{2T4CQSBKDAQ2KNDGOBRX34PZC3}

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	2026-05-18T04:33:29.482716Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d4f828482a1821a5346670637df1f916d34d20e6385b0b3d44082ccc2e6c223f

Aliases

arxiv: 0912.1915 · arxiv_version: 0912.1915v3 · doi: 10.48550/arxiv.0912.1915 · pith_short_12: 2T4CQSBKDAQ2 · pith_short_16: 2T4CQSBKDAQ2KNDG · pith_short_8: 2T4CQSBK

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/2T4CQSBKDAQ2KNDGOBRX34PZC3 \
  | 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: d4f828482a1821a5346670637df1f916d34d20e6385b0b3d44082ccc2e6c223f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a9baf4aed0bb21c1d25e9d89f5180da63fa1d659fd23d0ecd428240849b8e6c",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-12-10T05:00:59Z",
    "title_canon_sha256": "17d5abcf3c448c3bfa0e5e58f1ee729563e4823690d0e4c6d8f232fb4ce7f34e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.1915",
    "kind": "arxiv",
    "version": 3
  }
}