Pith Number

pith:HAJ6I5RI

pith:2015:HAJ6I5RIJSH7W3M4IVX5EPQC3C

not attested not anchored not stored refs pending

Approximate polynomial structure in additively large sets

Isaac Goldbring, Karl Mahlburg, Martino Lupini, Mauro Di Nasso, Renling Jin, Steven Leth

arxiv:1508.02350 v1 · 2015-08-10 · math.CO · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HAJ6I5RIJSH7W3M4IVX5EPQC3C}

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	2026-05-18T01:01:42.313878Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3813e476284c8ffb6d9c456fd23e02d8a36591253331fafe1c04f9556dc8b254

Aliases

arxiv: 1508.02350 · arxiv_version: 1508.02350v1 · doi: 10.48550/arxiv.1508.02350 · pith_short_12: HAJ6I5RIJSH7 · pith_short_16: HAJ6I5RIJSH7W3M4 · pith_short_8: HAJ6I5RI

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/HAJ6I5RIJSH7W3M4IVX5EPQC3C \
  | 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: 3813e476284c8ffb6d9c456fd23e02d8a36591253331fafe1c04f9556dc8b254

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8809a294d109ef4d91e2dcd32109e30521a7a15322ab4d92771dc45f37d11a73",
    "cross_cats_sorted": [
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-08-10T18:41:28Z",
    "title_canon_sha256": "f754bc3a9c46af864ccc3edf96d6b1b94f925c1221724952dd8770ee1fa8faaf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.02350",
    "kind": "arxiv",
    "version": 1
  }
}