Pith Number

pith:P4CDKMNY

pith:2020:P4CDKMNYGWVSSFDYRV47KB3A47

not attested not anchored not stored refs pending

Apollonius surfaces, circumscribed spheres of tetrahedra, Menelaus' and Ceva's theorems in $\SXR$ and $\HXR$ geometries

Jen\H{o} Szirmai

arxiv:2012.06155 v1 · 2020-12-11 · math.MG

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P4CDKMNYGWVSSFDYRV47KB3A47}

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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	2026-07-05T01:58:48.370927Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f043531b835ab2914788d79f50760e7fcf314791e7ce2f411544d49497db8ea

Aliases

arxiv: 2012.06155 · arxiv_version: 2012.06155v1 · doi: 10.48550/arxiv.2012.06155 · pith_short_12: P4CDKMNYGWVS · pith_short_16: P4CDKMNYGWVSSFDY · pith_short_8: P4CDKMNY

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/P4CDKMNYGWVSSFDYRV47KB3A47 \
  | 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: 7f043531b835ab2914788d79f50760e7fcf314791e7ce2f411544d49497db8ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b45ba914a55e631c8ec60452987beba70f5a79d8c2d0ba15574be81bb35886fd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2020-12-11T06:32:06Z",
    "title_canon_sha256": "73292a3006e8e32f68647d5d835521bbbc88fa2df4b8037121f778e8ead78ab5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2012.06155",
    "kind": "arxiv",
    "version": 1
  }
}