Pith Number

pith:67QSM6YZ

pith:2009:67QSM6YZHE4XVVEEY5HP6NKNIA

not attested not anchored not stored refs pending

Positivity theorems for solid-angle polynomials

Matthias Beck, Sinai Robins, Steven V Sam

arxiv:0906.4031 v3 · 2009-06-22 · math.CO · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{67QSM6YZHE4XVVEEY5HP6NKNIA}

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	2026-05-18T01:37:51.654535Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7e1267b1939397ad484c74eff354d401dd8f012f1a65c4c54b23ed42e912ece

Aliases

arxiv: 0906.4031 · arxiv_version: 0906.4031v3 · doi: 10.48550/arxiv.0906.4031 · pith_short_12: 67QSM6YZHE4X · pith_short_16: 67QSM6YZHE4XVVEE · pith_short_8: 67QSM6YZ

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/67QSM6YZHE4XVVEEY5HP6NKNIA \
  | 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: f7e1267b1939397ad484c74eff354d401dd8f012f1a65c4c54b23ed42e912ece

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18d01996cf6bbe0deea503de38365432a5a1811896ea864461b49be91fa19e90",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-06-22T15:07:33Z",
    "title_canon_sha256": "8e7fd3155889f0a9491e89aa19e760987561a038d5da2906379307d2e51f6019"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.4031",
    "kind": "arxiv",
    "version": 3
  }
}