Pith Number

pith:HL3O5DEB

pith:2008:HL3O5DEBSP2GMIIJ76EZB54LRI

not attested not anchored not stored refs pending

A converse to the Grace--Walsh--Szeg\H{o} theorem

David G. Wagner, Petter Br\"and\'en

arxiv:0809.3225 v1 · 2008-09-18 · math.CV · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HL3O5DEBSP2GMIIJ76EZB54LRI}

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	2026-05-18T02:15:34.294591Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3af6ee8c8193f4662109ff8990f78b8a3b99caeec9509e2aed18e3f80167d7e3

Aliases

arxiv: 0809.3225 · arxiv_version: 0809.3225v1 · doi: 10.48550/arxiv.0809.3225 · pith_short_12: HL3O5DEBSP2G · pith_short_16: HL3O5DEBSP2GMIIJ · pith_short_8: HL3O5DEB

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/HL3O5DEBSP2GMIIJ76EZB54LRI \
  | 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: 3af6ee8c8193f4662109ff8990f78b8a3b99caeec9509e2aed18e3f80167d7e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9f500af0283a1f41b1d0b6ba6bc16850965ec392d5aeafa82e7343a1d1ce33fa",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2008-09-18T18:46:40Z",
    "title_canon_sha256": "3561fde255f272d3184a3982ce6cdd080abe9101cd855b5408aa2d1cb4bc5b3e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0809.3225",
    "kind": "arxiv",
    "version": 1
  }
}