Pith Number

pith:MYKDNXJR

pith:2026:MYKDNXJR3QS4SPFBEXT4R3QEMO

not attested not anchored not stored refs pending

A global shadow lemma for relatively Morse groups in higher rank

Dongryul M. Kim, Hee Oh

arxiv:2606.19779 v1 · 2026-06-18 · math.GT · math.DS · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MYKDNXJR3QS4SPFBEXT4R3QEMO}

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	2026-06-19T16:12:34.934550Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

661436dd31dc25c93ca125e7c8ee0463a04bf46f0abb92f4a622fcb1da8ec4df

Aliases

arxiv: 2606.19779 · arxiv_version: 2606.19779v1 · doi: 10.48550/arxiv.2606.19779 · pith_short_12: MYKDNXJR3QS4 · pith_short_16: MYKDNXJR3QS4SPFB · pith_short_8: MYKDNXJR

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/MYKDNXJR3QS4SPFBEXT4R3QEMO \
  | 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: 661436dd31dc25c93ca125e7c8ee0463a04bf46f0abb92f4a622fcb1da8ec4df

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e9e97f8b32bc964c8beefa5f4f470425493b901d56b9a07e11bb3ee1c534cb3",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-06-18T04:28:18Z",
    "title_canon_sha256": "5d700a69bb35e068f18189cd127c039ec03db9cd20f702887d74e4902c0fc7c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.19779",
    "kind": "arxiv",
    "version": 1
  }
}