Pith Number

pith:VFRV3ONV

pith:2012:VFRV3ONVSAEL7SPBOFNVTDFN6I

not attested not anchored not stored refs pending

Formulating Szemer\'edi's Theorem in Terms of Ultrafilters

Heinrich-Gregor Zirnstein

arxiv:1206.0967 v1 · 2012-06-05 · math.FA · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VFRV3ONVSAEL7SPBOFNVTDFN6I}

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	2026-05-18T03:54:15.647300Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9635db9b59008bfc9e1715b598cadf22a0fccfbcecbf9a7ee3e06d7f7bdc636

Aliases

arxiv: 1206.0967 · arxiv_version: 1206.0967v1 · doi: 10.48550/arxiv.1206.0967 · pith_short_12: VFRV3ONVSAEL · pith_short_16: VFRV3ONVSAEL7SPB · pith_short_8: VFRV3ONV

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/VFRV3ONVSAEL7SPBOFNVTDFN6I \
  | 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: a9635db9b59008bfc9e1715b598cadf22a0fccfbcecbf9a7ee3e06d7f7bdc636

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac1e9394e8f2d9f3c10f28bb1232c2d0a75900a5e0dcf2213cc188346b4ea3be",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-06-05T15:44:32Z",
    "title_canon_sha256": "73f2afa5cbecb8268c3824071ce2512aadfd3513f5e5e06f3c92060a1047b675"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.0967",
    "kind": "arxiv",
    "version": 1
  }
}