Pith Number

pith:L7EM5K7Q

pith:2016:L7EM5K7QB4DQSUUQKCP5TC73ZE

not attested not anchored not stored refs pending

The three gap theorem and the space of lattices

Andreas Str\"ombergsson, Jens Marklof

arxiv:1612.04906 v2 · 2016-12-15 · 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{L7EM5K7QB4DQSUUQKCP5TC73ZE}

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	2026-05-18T00:41:53.302450Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5fc8ceabf00f07095290509fd98bfbc9075451c666d3cb97b7f4d8be8fc93c77

Aliases

arxiv: 1612.04906 · arxiv_version: 1612.04906v2 · doi: 10.48550/arxiv.1612.04906 · pith_short_12: L7EM5K7QB4DQ · pith_short_16: L7EM5K7QB4DQSUUQ · pith_short_8: L7EM5K7Q

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/L7EM5K7QB4DQSUUQKCP5TC73ZE \
  | 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: 5fc8ceabf00f07095290509fd98bfbc9075451c666d3cb97b7f4d8be8fc93c77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d80da5b62eea7b60c67947e6beb2531c2ddcf989aeef7f6b32a05f87ae4cc072",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-12-15T02:07:41Z",
    "title_canon_sha256": "948cdde927d2d3fb7526c37ce00027d9b04d7a7d91f0152519f14e5fee5ab130"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.04906",
    "kind": "arxiv",
    "version": 2
  }
}