Pith Number

pith:VTQYJVCY

pith:2011:VTQYJVCYCRVL7MWSR6A7N5JUBX

not attested not anchored not stored refs pending

Ehrhart's polynomial for equilateral triangles in $\mathbb Z^3$

Eugen J. Ionascu

arxiv:1107.0695 v2 · 2011-07-04 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VTQYJVCYCRVL7MWSR6A7N5JUBX}

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	2026-05-18T04:18:34.252931Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ace184d458146abfb2d28f81f6f5340df0ad25e64ee880c0010153af72415ee4

Aliases

arxiv: 1107.0695 · arxiv_version: 1107.0695v2 · doi: 10.48550/arxiv.1107.0695 · pith_short_12: VTQYJVCYCRVL · pith_short_16: VTQYJVCYCRVL7MWS · pith_short_8: VTQYJVCY

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/VTQYJVCYCRVL7MWSR6A7N5JUBX \
  | 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: ace184d458146abfb2d28f81f6f5340df0ad25e64ee880c0010153af72415ee4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ace2aed91f9fe67e33e7b1d94361efa6623075553c3455a791542be03de18c64",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-07-04T18:22:38Z",
    "title_canon_sha256": "38e6816b5bfcd71d1a79fc9c766b491b9974e39340ffa6b88510fdfd7de529a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.0695",
    "kind": "arxiv",
    "version": 2
  }
}