Pith Number

pith:OGRXBAAQ

pith:2010:OGRXBAAQRLW4Y7BL4YZX4QXM72

not attested not anchored not stored refs pending

Periodicity in the stable representation theory of crystallographic groups

Daniel A. Ramras

arxiv:1007.0406 v4 · 2010-07-02 · 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{OGRXBAAQRLW4Y7BL4YZX4QXM72}

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	2026-05-18T00:16:39.374587Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

71a37080108aedcc7c2be6337e42ecfeab8e18bdf058aa6163722608c11a7399

Aliases

arxiv: 1007.0406 · arxiv_version: 1007.0406v4 · doi: 10.48550/arxiv.1007.0406 · pith_short_12: OGRXBAAQRLW4 · pith_short_16: OGRXBAAQRLW4Y7BL · pith_short_8: OGRXBAAQ

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/OGRXBAAQRLW4Y7BL4YZX4QXM72 \
  | 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: 71a37080108aedcc7c2be6337e42ecfeab8e18bdf058aa6163722608c11a7399

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dcb385217ec0040771b6c3e5ec2a1ec7801eb03bd27790b9366afe2cdeb0675a",
    "cross_cats_sorted": [
      "math.AT",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2010-07-02T17:20:00Z",
    "title_canon_sha256": "f47a7a94a85a39d207662d47c47fc39013fbca8b0ff850cefd1d473fd79c0c74"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.0406",
    "kind": "arxiv",
    "version": 4
  }
}