Pith Number

pith:UJQRT3KU

pith:2017:UJQRT3KU5FHWFH7EKIPKUIPQRW

not attested not anchored not stored refs pending

Invariant measures for the actions of the modular group

Shilei Fan, Yanqi Qiu

arxiv:1703.03086 v3 · 2017-03-09 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UJQRT3KU5FHWFH7EKIPKUIPQRW}

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	2026-05-18T00:42:51.222922Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a26119ed54e94f629fe4521eaa21f08d9cc1227e372b4b48533165cc4c8cf917

Aliases

arxiv: 1703.03086 · arxiv_version: 1703.03086v3 · doi: 10.48550/arxiv.1703.03086 · pith_short_12: UJQRT3KU5FHW · pith_short_16: UJQRT3KU5FHWFH7E · pith_short_8: UJQRT3KU

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/UJQRT3KU5FHWFH7EKIPKUIPQRW \
  | 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: a26119ed54e94f629fe4521eaa21f08d9cc1227e372b4b48533165cc4c8cf917

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b3f6763395c792ec40f8b5530557cb6716a57ee27cbcbc89e2b0bc7c63f49e46",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-03-09T00:38:59Z",
    "title_canon_sha256": "d6f40cf837915baec0554526622d5724cb4b7c080c0dfa51a12fca28fc48a3b5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1703.03086",
    "kind": "arxiv",
    "version": 3
  }
}