Pith Number

pith:B5MGA2TZ

pith:2019:B5MGA2TZMI3SS5GDOMYURTDQAQ

not attested not anchored not stored refs pending

Density theorems for GL(n)

Valentin Blomer

arxiv:1906.07459 v2 · 2019-06-18 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B5MGA2TZMI3SS5GDOMYURTDQAQ}

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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.

Cited by

1 paper in Pith

A density theorem for Borel-Type Congruence subgroups and arithmetic applications

Receipt and verification

First computed	2026-07-05T05:14:54.197420Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f58606a7962372974c3733148cc70042d97bbc75b36eef3e68d6a79e4258236

Aliases

arxiv: 1906.07459 · arxiv_version: 1906.07459v2 · doi: 10.48550/arxiv.1906.07459 · pith_short_12: B5MGA2TZMI3S · pith_short_16: B5MGA2TZMI3SS5GD · pith_short_8: B5MGA2TZ

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/B5MGA2TZMI3SS5GDOMYURTDQAQ \
  | 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: 0f58606a7962372974c3733148cc70042d97bbc75b36eef3e68d6a79e4258236

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "abfb70428baa471876b6f7e862e4803fd79840720a63ef581b413e2a43d40c82",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-06-18T09:27:45Z",
    "title_canon_sha256": "dbe11254400e2cace9fcd1e04e50c6531adde0fdda674ecce0a8fae1fc8f8134"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.07459",
    "kind": "arxiv",
    "version": 2
  }
}