Pith Number

pith:Z26S4VK2

pith:2015:Z26S4VK2F23NQ5O3NF77A4BV5E

not attested not anchored not stored refs pending

Tiling, circle packing and exponential sums over finite fields

A. Iosevich, C.D. Haessig, J. Pakianathan, L. Vaicunas, S. Robins

arxiv:1507.05861 v1 · 2015-07-21 · math.CO · math.CA · 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{Z26S4VK2F23NQ5O3NF77A4BV5E}

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	2026-05-18T01:36:32.236561Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cebd2e555a2eb6d875db697ff07035e93d1a514d063747994692bb4cb7f50cf0

Aliases

arxiv: 1507.05861 · arxiv_version: 1507.05861v1 · doi: 10.48550/arxiv.1507.05861 · pith_short_12: Z26S4VK2F23N · pith_short_16: Z26S4VK2F23NQ5O3 · pith_short_8: Z26S4VK2

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/Z26S4VK2F23NQ5O3NF77A4BV5E \
  | 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: cebd2e555a2eb6d875db697ff07035e93d1a514d063747994692bb4cb7f50cf0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2643f69e72cf5ead54bd0d5aac57f115f6996a4735fdb238ee0776ec2850bda5",
    "cross_cats_sorted": [
      "math.CA",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-07-21T14:53:22Z",
    "title_canon_sha256": "1cf22a43d32dd2e927e3bf6f447773c10caa0d99fd3bd0a18bc739905e422a65"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.05861",
    "kind": "arxiv",
    "version": 1
  }
}