Pith Number

pith:3QG776J5

pith:2016:3QG776J5VAAYGFL3445JXCR4DF

not attested not anchored not stored refs pending

Approximate lattices

Michael Bj\"orklund, Tobias Hartnick

arxiv:1612.09246 v2 · 2016-12-29 · math.GR · math.DS · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3QG776J5VAAYGFL3445JXCR4DF}

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.

Cited by

1 paper in Pith

On almost periodicity in crystalline measures

Receipt and verification

First computed	2026-05-18T00:00:46.010443Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc0dfff93da80183157be73a9b8a3c19679ee534442c9cf4fb8166cc182bf563

Aliases

arxiv: 1612.09246 · arxiv_version: 1612.09246v2 · doi: 10.48550/arxiv.1612.09246 · pith_short_12: 3QG776J5VAAY · pith_short_16: 3QG776J5VAAYGFL3 · pith_short_8: 3QG776J5

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/3QG776J5VAAYGFL3445JXCR4DF \
  | 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: dc0dfff93da80183157be73a9b8a3c19679ee534442c9cf4fb8166cc182bf563

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40d6902f107a35667caba9e83c54ea4343e787601320064b3e80aef615b2fccb",
    "cross_cats_sorted": [
      "math.DS",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-12-29T19:01:04Z",
    "title_canon_sha256": "ffce1cbc4fd315c4d438449271bed86b0af362f420f3c96be99fe6b2c485dc5c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.09246",
    "kind": "arxiv",
    "version": 2
  }
}