Pith Number

pith:333MGRTR

pith:2012:333MGRTRKNDFTG2RJ3PTWVHP6T

not attested not anchored not stored refs pending

The Lower Algebraic K-Theory of Split Three-Dimensional Crystallographic Groups

Daniel Farley, Ivonne J. Ortiz

arxiv:1211.2024 v1 · 2012-11-09 · math.KT · math.AT · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{333MGRTRKNDFTG2RJ3PTWVHP6T}

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	2026-05-18T03:41:11.941132Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

def6c346715346599b514edf3b54eff4ccaa2470b04342a418078be88732efe1

Aliases

arxiv: 1211.2024 · arxiv_version: 1211.2024v1 · doi: 10.48550/arxiv.1211.2024 · pith_short_12: 333MGRTRKNDF · pith_short_16: 333MGRTRKNDFTG2R · pith_short_8: 333MGRTR

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/333MGRTRKNDFTG2RJ3PTWVHP6T \
  | 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: def6c346715346599b514edf3b54eff4ccaa2470b04342a418078be88732efe1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cbd78dc9062c0980af96f64524e42d5d5428767ed7886d6d560fe7f00b0d7406",
    "cross_cats_sorted": [
      "math.AT",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2012-11-09T02:01:22Z",
    "title_canon_sha256": "eecc08892e7c2ad3be2bf0b37e48186feac30d80f4b9e913016260d1b7a8aca0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.2024",
    "kind": "arxiv",
    "version": 1
  }
}