Pith Number

pith:JGX77OR5

pith:2025:JGX77OR56TZ3LYBGKRBL6LCUS7

not attested not anchored not stored refs pending

A strong height gap theorem for $PGL_2$

Mikhail Belolipetsky, Sebastian Hurtado

arxiv:2507.22266 v1 · 2025-07-29 · 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{JGX77OR56TZ3LYBGKRBL6LCUS7}

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	2026-07-05T11:45:19.353796Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

49afffba3df4f3b5e0265442bf2c5497dd9d03d114f5d9883be70968cf3441e5

Aliases

arxiv: 2507.22266 · arxiv_version: 2507.22266v1 · doi: 10.48550/arxiv.2507.22266 · pith_short_12: JGX77OR56TZ3 · pith_short_16: JGX77OR56TZ3LYBG · pith_short_8: JGX77OR5

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/JGX77OR56TZ3LYBGKRBL6LCUS7 \
  | 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: 49afffba3df4f3b5e0265442bf2c5497dd9d03d114f5d9883be70968cf3441e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e0b63136e635ce2cb776b87d25a2103f1aa384f5f9ccb17c7eb2f4bfc032eba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2025-07-29T22:35:37Z",
    "title_canon_sha256": "55b5932ae3ea10f3ac7729c52d2e198e59ffcc9d7d4f0fd5b55bd49c8a5bc071"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.22266",
    "kind": "arxiv",
    "version": 1
  }
}