Pith Number

pith:4DYCEKAT

pith:2014:4DYCEKAT74LEPPT6GNKOJCHKU6

not attested not anchored not stored refs pending

Beyond Expansion II: Low-Lying Fundamental Geodesics

Alex Kontorovich, Jean Bourgain

arxiv:1406.1366 v2 · 2014-06-05 · math.NT · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4DYCEKAT74LEPPT6GNKOJCHKU6}

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	2026-05-18T01:12:15.100679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0f0222813ff1647be7e3354e488eaa79f70eac239bc8455476ebe88ff04d142

Aliases

arxiv: 1406.1366 · arxiv_version: 1406.1366v2 · doi: 10.48550/arxiv.1406.1366 · pith_short_12: 4DYCEKAT74LE · pith_short_16: 4DYCEKAT74LEPPT6 · pith_short_8: 4DYCEKAT

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/4DYCEKAT74LEPPT6GNKOJCHKU6 \
  | 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: e0f0222813ff1647be7e3354e488eaa79f70eac239bc8455476ebe88ff04d142

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fdf2212efc39bc7ddaa835532e615fa24f913583b1666ad44c21de79981119ee",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-06-05T12:49:48Z",
    "title_canon_sha256": "707e23753b1e2495fc39a15fc87ac0790c53854f802581723b08a4c7b0fbfc2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1406.1366",
    "kind": "arxiv",
    "version": 2
  }
}