Pith Number

pith:VP4STN4F

pith:2014:VP4STN4FZGRREZ74NWNZA5U6DR

not attested not anchored not stored refs pending

On the trace formula for Hecke operators on congruence subgroups

Alexandru A. Popa

arxiv:1408.4998 v4 · 2014-08-21 · 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{VP4STN4FZGRREZ74NWNZA5U6DR}

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	2026-05-18T00:42:49.208503Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abf929b785c9a31267fc6d9b90769e1c5ae192576fbd0b71a4af67664745d6b1

Aliases

arxiv: 1408.4998 · arxiv_version: 1408.4998v4 · doi: 10.48550/arxiv.1408.4998 · pith_short_12: VP4STN4FZGRR · pith_short_16: VP4STN4FZGRREZ74 · pith_short_8: VP4STN4F

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/VP4STN4FZGRREZ74NWNZA5U6DR \
  | 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: abf929b785c9a31267fc6d9b90769e1c5ae192576fbd0b71a4af67664745d6b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1cf93b2e1a1b03e29128084885673828002d7101672d5340eeb5254711a94172",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-08-21T13:26:28Z",
    "title_canon_sha256": "5cde050a592fa199d6a235930b9ecb288df48a8f0b1fb7da53598b97533be1d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.4998",
    "kind": "arxiv",
    "version": 4
  }
}