Pith Number

pith:XYVIVQ3P

pith:2015:XYVIVQ3PWAJCOQYD3P4MKZNXLX

not attested not anchored not stored refs pending

Milnor-type theorems for left-invariant Riemannian metrics on Lie groups

Hiroshi Tamaru, Kazuhiro Terada, Takahiro Hashinaga

arxiv:1501.02485 v1 · 2015-01-11 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XYVIVQ3PWAJCOQYD3P4MKZNXLX}

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	2026-05-18T02:29:37.847036Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be2a8ac36fb012274303dbf8c565b75defd4615d55b336a9e625afdf7bef6282

Aliases

arxiv: 1501.02485 · arxiv_version: 1501.02485v1 · doi: 10.48550/arxiv.1501.02485 · pith_short_12: XYVIVQ3PWAJC · pith_short_16: XYVIVQ3PWAJCOQYD · pith_short_8: XYVIVQ3P

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/XYVIVQ3PWAJCOQYD3P4MKZNXLX \
  | 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: be2a8ac36fb012274303dbf8c565b75defd4615d55b336a9e625afdf7bef6282

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f82e0d496620c12192b26acb7c142e09305d50701768b08edf7f1ac0b3eae3a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-01-11T18:58:03Z",
    "title_canon_sha256": "f89bf58c8c3886de49c199baac55cbceeeb92ec37b2271079fe1da49e214da80"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.02485",
    "kind": "arxiv",
    "version": 1
  }
}