Pith Number

pith:ZTXUTW2U

pith:2016:ZTXUTW2UM3O42F34CFWTS4DYVT

not attested not anchored not stored refs pending

Harmonic analysis for real spherical spaces

Bernhard Kr\"otz, Henrik Schlichtkrull

arxiv:1612.01841 v2 · 2016-12-06 · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZTXUTW2UM3O42F34CFWTS4DYVT}

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	2026-05-18T00:14:57.253093Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ccef49db5466ddcd177c116d397078acecda32d3b1f6b7aae7b6d330c797c7a8

Aliases

arxiv: 1612.01841 · arxiv_version: 1612.01841v2 · doi: 10.48550/arxiv.1612.01841 · pith_short_12: ZTXUTW2UM3O4 · pith_short_16: ZTXUTW2UM3O42F34 · pith_short_8: ZTXUTW2U

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/ZTXUTW2UM3O42F34CFWTS4DYVT \
  | 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: ccef49db5466ddcd177c116d397078acecda32d3b1f6b7aae7b6d330c797c7a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7922c8dccec961d7db2f1a7f66346440c91d0f6805747e86bed4a7551b76324e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2016-12-06T14:59:40Z",
    "title_canon_sha256": "8199423a3641325f7d6c9d469a1be8b0cfa0fa2e19b734f154afb69482fc2603"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.01841",
    "kind": "arxiv",
    "version": 2
  }
}