Pith Number

pith:VKGV7CWI

pith:2012:VKGV7CWIOVJ7QOWZYPPSDPUAXZ

not attested not anchored not stored refs pending

Convergence results for systems of linear forms on cyclic groups, and periodic nilsequences

Olof Sisask, Pablo Candela

arxiv:1212.3681 v2 · 2012-12-15 · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VKGV7CWIOVJ7QOWZYPPSDPUAXZ}

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	2026-05-18T02:43:09.515936Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa8d5f8ac87553f83ad9c3df21be80be5590150f53aaacf75910b43b101cb8da

Aliases

arxiv: 1212.3681 · arxiv_version: 1212.3681v2 · doi: 10.48550/arxiv.1212.3681 · pith_short_12: VKGV7CWIOVJ7 · pith_short_16: VKGV7CWIOVJ7QOWZ · pith_short_8: VKGV7CWI

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/VKGV7CWIOVJ7QOWZYPPSDPUAXZ \
  | 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: aa8d5f8ac87553f83ad9c3df21be80be5590150f53aaacf75910b43b101cb8da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0977a21a4eb2003b6ed04d9d89e1b89ad9e365db5fd9b1adf33530b60327c1c6",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-12-15T13:13:27Z",
    "title_canon_sha256": "e0631c494d57c335b0ce40ca3748b6a08f344f23c4c553ffa944cbb6b3affbc3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.3681",
    "kind": "arxiv",
    "version": 2
  }
}