Pith Number

pith:V6ZF2X3S

pith:2015:V6ZF2X3SKJEBLZCJ5S7Q6HOTAQ

not attested not anchored not stored refs pending

Lattice Point Counting in Sectors of Hyperbolic 3-space

Niko Laaksonen

arxiv:1511.00580 v1 · 2015-11-02 · 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{V6ZF2X3SKJEBLZCJ5S7Q6HOTAQ}

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	2026-05-18T00:28:38.228506Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

afb25d5f72524815e449ecbf0f1dd30419f9e7a91f58a8c2e30a450f6d3d843f

Aliases

arxiv: 1511.00580 · arxiv_version: 1511.00580v1 · doi: 10.48550/arxiv.1511.00580 · pith_short_12: V6ZF2X3SKJEB · pith_short_16: V6ZF2X3SKJEBLZCJ · pith_short_8: V6ZF2X3S

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/V6ZF2X3SKJEBLZCJ5S7Q6HOTAQ \
  | 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: afb25d5f72524815e449ecbf0f1dd30419f9e7a91f58a8c2e30a450f6d3d843f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e32302442c03747197ce85aac1a28e44376b30a5930001dcf2816bdf5478ba63",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-11-02T16:53:56Z",
    "title_canon_sha256": "66238ea11eb63a60e348fc28469201abd4bafe30042256842ded5013fef532b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.00580",
    "kind": "arxiv",
    "version": 1
  }
}