Pith Number

pith:GPBJF7JU

pith:2016:GPBJF7JUXRO3LCCASR2TZAP7PX

not attested not anchored not stored refs pending

Degree, mixing, and absolutely continuous spectrum of cocycles with values in compact Lie groups

Rafael Tiedra de Aldecoa

arxiv:1605.04198 v1 · 2016-05-13 · math.DS · math-ph · math.MP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GPBJF7JUXRO3LCCASR2TZAP7PX}

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	2026-05-18T01:14:54.044139Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

33c292fd34bc5db5884094753c81ff7df2e2d20cce8a10691e8ceb396facc899

Aliases

arxiv: 1605.04198 · arxiv_version: 1605.04198v1 · doi: 10.48550/arxiv.1605.04198 · pith_short_12: GPBJF7JUXRO3 · pith_short_16: GPBJF7JUXRO3LCCA · pith_short_8: GPBJF7JU

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/GPBJF7JUXRO3LCCASR2TZAP7PX \
  | 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: 33c292fd34bc5db5884094753c81ff7df2e2d20cce8a10691e8ceb396facc899

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed1cfea1dc921e8a62105bdc468dd5cc3f3a900c836fea2c152139835e9e8d73",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-05-13T14:49:09Z",
    "title_canon_sha256": "75b3e036e2f436c12fb7ad1bad3f2400c37770d9a3d4ce877772bfaee951f01d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.04198",
    "kind": "arxiv",
    "version": 1
  }
}