Pith Number

pith:MSMKLHNB

pith:2023:MSMKLHNBRCVWIGWDFRSDEX4J5J

not attested not anchored not stored refs pending

A translation of N.M. Katz's "Exponential Sums"

David T. Nguyen

arxiv:2308.11611 v1 · 2023-08-13 · math.NT · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MSMKLHNBRCVWIGWDFRSDEX4J5J}

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	2026-07-05T06:46:07.655098Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6498a59da188ab641ac32c64325f89ea424787544cb5fd98fc9a7dd90bd8250b

Aliases

arxiv: 2308.11611 · arxiv_version: 2308.11611v1 · doi: 10.48550/arxiv.2308.11611 · pith_short_12: MSMKLHNBRCVW · pith_short_16: MSMKLHNBRCVWIGWD · pith_short_8: MSMKLHNB

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/MSMKLHNBRCVWIGWDFRSDEX4J5J \
  | 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: 6498a59da188ab641ac32c64325f89ea424787544cb5fd98fc9a7dd90bd8250b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3468f668eab23d0a5b3bac395bb7177178978f1cdaa7af2dfdf884ac120ec5af",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2023-08-13T18:18:40Z",
    "title_canon_sha256": "3b7e8926a075868d1a899d2cbc7a21922c0d8fb4afc6cd30bdc75380119739b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2308.11611",
    "kind": "arxiv",
    "version": 1
  }
}