Pith Number

pith:4MUJL3X4

pith:2015:4MUJL3X4TTO2SQ32MBP5N2GBTR

not attested not anchored not stored refs pending

Three-Dimensional Projective Geometry with Geometric Algebra

Changpeng Shao, Hongbo Li, Lei Dong, Lei Huang

arxiv:1507.06634 v1 · 2015-07-11 · math.MG · cs.CG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4MUJL3X4TTO2SQ32MBP5N2GBTR}

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	2026-05-18T01:36:23.083213Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e32895eefc9cdda9437a605fd6e8c19c426d72618acb1648a86f59f9ab3a1fc4

Aliases

arxiv: 1507.06634 · arxiv_version: 1507.06634v1 · doi: 10.48550/arxiv.1507.06634 · pith_short_12: 4MUJL3X4TTO2 · pith_short_16: 4MUJL3X4TTO2SQ32 · pith_short_8: 4MUJL3X4

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/4MUJL3X4TTO2SQ32MBP5N2GBTR \
  | 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: e32895eefc9cdda9437a605fd6e8c19c426d72618acb1648a86f59f9ab3a1fc4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8106b30040e5868640f32a2742d62d27682e88b0980283ce51f984a9db1a512c",
    "cross_cats_sorted": [
      "cs.CG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2015-07-11T19:05:28Z",
    "title_canon_sha256": "7382af590be55564b60fb7f0c89f564c6b9c6e658d203f237b8f142a054604d3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.06634",
    "kind": "arxiv",
    "version": 1
  }
}