Pith Number

pith:O7EVB3G2

pith:2013:O7EVB3G2L5HBEE6X33GE6TWC4D

not attested not anchored not stored refs pending

A note on some special exponential sums

Xiwang Cao

arxiv:1311.2117 v1 · 2013-11-09 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{O7EVB3G2L5HBEE6X33GE6TWC4D}

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	2026-05-18T03:07:33.502339Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

77c950ecda5f4e1213d7decc4f4ec2e0e4ca6fb403f0534539d9360b75231340

Aliases

arxiv: 1311.2117 · arxiv_version: 1311.2117v1 · doi: 10.48550/arxiv.1311.2117 · pith_short_12: O7EVB3G2L5HB · pith_short_16: O7EVB3G2L5HBEE6X · pith_short_8: O7EVB3G2

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/O7EVB3G2L5HBEE6X33GE6TWC4D \
  | 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: 77c950ecda5f4e1213d7decc4f4ec2e0e4ca6fb403f0534539d9360b75231340

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6c76a1f2a51d4197b4d763d0da1e2fa1193b0cb74a8aefc29b3988cf2214e13",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-11-09T00:58:50Z",
    "title_canon_sha256": "11adb8f279d88173d4fc4124f9228e6a580f6806e746b336320012d6c61a6550"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.2117",
    "kind": "arxiv",
    "version": 1
  }
}