Pith Number

pith:76ITIK5I

pith:2013:76ITIK5I6IJQ645H5JAFM2ZWCF

not attested not anchored not stored refs pending

Frameworks with forced symmetry II: Orientation-preserving crystallographic groups

Justin Malestein, Louis Theran

arxiv:1304.0756 v2 · 2013-04-01 · math.MG · 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{76ITIK5I6IJQ645H5JAFM2ZWCF}

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	2026-05-18T03:22:16.918400Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff91342ba8f2130f73a7ea40566b361141e18c28b0861e6f0f51a2662e686779

Aliases

arxiv: 1304.0756 · arxiv_version: 1304.0756v2 · doi: 10.48550/arxiv.1304.0756 · pith_short_12: 76ITIK5I6IJQ · pith_short_16: 76ITIK5I6IJQ645H · pith_short_8: 76ITIK5I

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/76ITIK5I6IJQ645H5JAFM2ZWCF \
  | 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: ff91342ba8f2130f73a7ea40566b361141e18c28b0861e6f0f51a2662e686779

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2cdeb1481536956a0f3dfcd0de94f594c240a547cf24d99a38ac6dcbdc88e204",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2013-04-01T17:30:59Z",
    "title_canon_sha256": "aceb1c03a0b2899f27440c798e69cdddedf382a5482bab402d8f4453b4a336b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.0756",
    "kind": "arxiv",
    "version": 2
  }
}