Pith Number

pith:2MKGOOOG

pith:2023:2MKGOOOGZJOIS5QRS3UDMFNWPK

not attested not anchored not stored refs pending

Translation-like isoptic surfaces and angle sums of translation triangles in $\NIL$ geometry

G\'eza Csima, Jen\H{o} Szirmai

arxiv:2302.07653 v1 · 2023-02-15 · 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{2MKGOOOGZJOIS5QRS3UDMFNWPK}

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

Menelaus' and Ceva's theorems for translation triangles in Thurston geometries

Receipt and verification

First computed	2026-07-05T05:42:04.608648Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3146739c6ca5c89761196e83615b67aab71f29a46029d3383cf15a417c88a6a

Aliases

arxiv: 2302.07653 · arxiv_version: 2302.07653v1 · doi: 10.48550/arxiv.2302.07653 · pith_short_12: 2MKGOOOGZJOI · pith_short_16: 2MKGOOOGZJOIS5QR · pith_short_8: 2MKGOOOG

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/2MKGOOOGZJOIS5QRS3UDMFNWPK \
  | 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: d3146739c6ca5c89761196e83615b67aab71f29a46029d3383cf15a417c88a6a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5c75f4a8e40d83a374375fd01d06aa7529447af1a2adad6d7839850e1e2b658",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2023-02-15T13:37:29Z",
    "title_canon_sha256": "2af6a7b8c5a203289cd250af1b3312c3043fb3b1cbe4c6592ce911997162a44b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2302.07653",
    "kind": "arxiv",
    "version": 1
  }
}