Pith Number

pith:VQQEDX5V

pith:2006:VQQEDX5VOPVDWCOMH5SRA6IYMH

not attested not anchored not stored refs pending

Rigidity of p-adic cohomology classes of congruence subgroups of GL(n, Z)

Avner Ash, David Pollack, Glenn Stevens

arxiv:math/0609065 v1 · 2006-09-02 · 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{VQQEDX5VOPVDWCOMH5SRA6IYMH}

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	2026-05-18T02:57:45.532995Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac2041dfb573ea3b09cc3f6510791861dfb8bafedb608d450a1a3209adddf7e4

Aliases

arxiv: math/0609065 · arxiv_version: math/0609065v1 · doi: 10.48550/arxiv.math/0609065 · pith_short_12: VQQEDX5VOPVD · pith_short_16: VQQEDX5VOPVDWCOM · pith_short_8: VQQEDX5V

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/VQQEDX5VOPVDWCOMH5SRA6IYMH \
  | 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: ac2041dfb573ea3b09cc3f6510791861dfb8bafedb608d450a1a3209adddf7e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "16faac58f48f5e4ac91cf948c067cea19427a3e11e5234c2da1fecf8696c19dc",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2006-09-02T19:00:34Z",
    "title_canon_sha256": "d13887f7d6e901bf28af83546ee99b3f626806a79ab71fa5173a0738e28a7e8b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0609065",
    "kind": "arxiv",
    "version": 1
  }
}