Pith Number

pith:QRFMLLWX

pith:2025:QRFMLLWX457QOIMNH7LIAVJB6V

not attested not anchored not stored refs pending

Proper actions on finite products of hyperbolic spaces

Bingxue Tao, Renxing Wan

arxiv:2506.04856 v1 · 2025-06-05 · math.GR · 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{QRFMLLWX457QOIMNH7LIAVJB6V}

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	2026-07-05T11:17:00.602367Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

844ac5aed7e77f07218d3fd6805521f54f8d5489d2d439b04e1959346453a82c

Aliases

arxiv: 2506.04856 · arxiv_version: 2506.04856v1 · doi: 10.48550/arxiv.2506.04856 · pith_short_12: QRFMLLWX457Q · pith_short_16: QRFMLLWX457QOIMN · pith_short_8: QRFMLLWX

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/QRFMLLWX457QOIMNH7LIAVJB6V \
  | 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: 844ac5aed7e77f07218d3fd6805521f54f8d5489d2d439b04e1959346453a82c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ba7865586138589c81695bed499d2479b8c6d7975afbeacf788d0ffb3c90fef",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2025-06-05T10:24:42Z",
    "title_canon_sha256": "13075f032580541e6ea05eab585bd0b808b9a1dd51a544945ddcb3b373c0e4cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.04856",
    "kind": "arxiv",
    "version": 1
  }
}