Pith Number

pith:FNHFO7HX

pith:2015:FNHFO7HXVZSAFHXEXQV6C4V7W3

not attested not anchored not stored refs pending

Structure of sets which are well approximated by zero sets of harmonic polynomials

Matthew Badger, Max Engelstein, Tatiana Toro

arxiv:1509.03211 v2 · 2015-09-10 · math.CA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FNHFO7HXVZSAFHXEXQV6C4V7W3}

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	2026-05-18T00:21:00.238098Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b4e577cf7ae64029ee4bc2be172bfb6ecadc735c32d984ffd4e8c5f9c532284

Aliases

arxiv: 1509.03211 · arxiv_version: 1509.03211v2 · doi: 10.48550/arxiv.1509.03211 · pith_short_12: FNHFO7HXVZSA · pith_short_16: FNHFO7HXVZSAFHXE · pith_short_8: FNHFO7HX

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/FNHFO7HXVZSAFHXEXQV6C4V7W3 \
  | 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: 2b4e577cf7ae64029ee4bc2be172bfb6ecadc735c32d984ffd4e8c5f9c532284

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f47f88442bc02948a50b5a74f191cc07193878119890cf74ec5671378be500d9",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-09-10T16:12:44Z",
    "title_canon_sha256": "155bc3d449c07e2dcd6eca2c13b1a5a222140f213c4e23477a2c206ffff46868"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.03211",
    "kind": "arxiv",
    "version": 2
  }
}