Pith Number

pith:A4VVWAND

pith:2016:A4VVWANDEH7BQRXLY5VZFUZ2HN

not attested not anchored not stored refs pending

Eisenstein cycles as modular symbols

Debargha Banerjee, Loic Merel

arxiv:1609.04140 v1 · 2016-09-14 · 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{A4VVWANDEH7BQRXLY5VZFUZ2HN}

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	2026-05-18T00:19:04.472863Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

072b5b01a321fe1846ebc76b92d33a3b690c6957824f91bd5764a11e2c7d9bf6

Aliases

arxiv: 1609.04140 · arxiv_version: 1609.04140v1 · doi: 10.48550/arxiv.1609.04140 · pith_short_12: A4VVWANDEH7B · pith_short_16: A4VVWANDEH7BQRXL · pith_short_8: A4VVWAND

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/A4VVWANDEH7BQRXLY5VZFUZ2HN \
  | 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: 072b5b01a321fe1846ebc76b92d33a3b690c6957824f91bd5764a11e2c7d9bf6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8fc670e2c5e1517fcbe6da6c582d956e57e85bc4376c8d5dd048f67421075b48",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-09-14T05:22:23Z",
    "title_canon_sha256": "70c21bc82241be7f6e4489ff1c54f880705a8447e6f8e722a4058f9288b89565"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.04140",
    "kind": "arxiv",
    "version": 1
  }
}