Pith Number

pith:2Q5X7DD5

pith:2016:2Q5X7DD5QX573JW3OXQ44N2EX5

not attested not anchored not stored refs pending

Joint spectrum and infinite dihedral group

Rongwei Yang, Rostilav Grigorchuk

arxiv:1605.01547 v3 · 2016-05-05 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2Q5X7DD5QX573JW3OXQ44N2EX5}

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	2026-05-18T00:42:13.083930Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d43b7f8c7d85fbfda6db75e1ce3744bf45479925e2b7ae5e0a0650cd3bae71f0

Aliases

arxiv: 1605.01547 · arxiv_version: 1605.01547v3 · doi: 10.48550/arxiv.1605.01547 · pith_short_12: 2Q5X7DD5QX57 · pith_short_16: 2Q5X7DD5QX573JW3 · pith_short_8: 2Q5X7DD5

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/2Q5X7DD5QX573JW3OXQ44N2EX5 \
  | 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: d43b7f8c7d85fbfda6db75e1ce3744bf45479925e2b7ae5e0a0650cd3bae71f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "92aec9ba391cd4329ef52e922ef2aa2aae936781de3e605047c54dd5589e28bb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-05-05T10:43:09Z",
    "title_canon_sha256": "78bc879bbc3387c452f3a8664000c4b42ab6e330adfcdd55584f0a44797c2333"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.01547",
    "kind": "arxiv",
    "version": 3
  }
}