Pith Number

pith:V7K6NDMM

pith:2015:V7K6NDMMKUX6NOZ3WOR6XMNW4Y

not attested not anchored not stored refs pending

Spectral gaps, additive energy, and a fractal uncertainty principle

Joshua Zahl, Semyon Dyatlov

arxiv:1504.06589 v3 · 2015-04-24 · math.SP · math.AP · math.CO · math.DS · nlin.CD

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{V7K6NDMMKUX6NOZ3WOR6XMNW4Y}

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	2026-05-18T01:08:26.639271Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

afd5e68d8c552fe6bb3bb3a3ebb1b6e631549d29efd877b82a9babeaf7cf9d45

Aliases

arxiv: 1504.06589 · arxiv_version: 1504.06589v3 · doi: 10.48550/arxiv.1504.06589 · pith_short_12: V7K6NDMMKUX6 · pith_short_16: V7K6NDMMKUX6NOZ3 · pith_short_8: V7K6NDMM

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/V7K6NDMMKUX6NOZ3WOR6XMNW4Y \
  | 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: afd5e68d8c552fe6bb3bb3a3ebb1b6e631549d29efd877b82a9babeaf7cf9d45

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a72307ef880e79fdb822d08a065073acb620d2a3ae5e327596f37eb2692912dd",
    "cross_cats_sorted": [
      "math.AP",
      "math.CO",
      "math.DS",
      "nlin.CD"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2015-04-24T18:23:50Z",
    "title_canon_sha256": "b9662ad8cec2c9bc490ada153049c0f360fcac044857449e2a72eea2fcfed934"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.06589",
    "kind": "arxiv",
    "version": 3
  }
}