Pith Number

pith:T4BK6DWT

pith:2015:T4BK6DWTOEUJL265J2BB7WFO3P

not attested not anchored not stored refs pending

Sums of fractions modulo $p$

C. A. D\'iaz, M. Z. Garaev

arxiv:1510.07980 v1 · 2015-10-27 · 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{T4BK6DWTOEUJL265J2BB7WFO3P}

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	2026-05-18T01:28:44.917584Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f02af0ed3712895ebdd4e821fd8aedbd3efda11b6c73b579f746d0f20119edb

Aliases

arxiv: 1510.07980 · arxiv_version: 1510.07980v1 · doi: 10.48550/arxiv.1510.07980 · pith_short_12: T4BK6DWTOEUJ · pith_short_16: T4BK6DWTOEUJL265 · pith_short_8: T4BK6DWT

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/T4BK6DWTOEUJL265J2BB7WFO3P \
  | 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: 9f02af0ed3712895ebdd4e821fd8aedbd3efda11b6c73b579f746d0f20119edb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6e23f0f59da1529f304d1c9220bb33e79f5bce1f62f716826e2642605b1f705",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-10-27T16:45:12Z",
    "title_canon_sha256": "95d562905258a46ecb62d6f233087b39d145a339cf81dc9ce7bc066217a2ef01"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.07980",
    "kind": "arxiv",
    "version": 1
  }
}