Pith Number

pith:MFXYIVRT

pith:2011:MFXYIVRTHJGNCYBN6BLE7MXU4L

not attested not anchored not stored refs pending

On multiplicatively badly approximable numbers

Dzmitry Badziahin

arxiv:1101.1855 v1 · 2011-01-10 · 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{MFXYIVRTHJGNCYBN6BLE7MXU4L}

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	2026-05-18T03:02:44.287574Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

616f8456333a4cd1602df0564fb2f4e2f6cf781cf826ba7a71647182765fbbf4

Aliases

arxiv: 1101.1855 · arxiv_version: 1101.1855v1 · doi: 10.48550/arxiv.1101.1855 · pith_short_12: MFXYIVRTHJGN · pith_short_16: MFXYIVRTHJGNCYBN · pith_short_8: MFXYIVRT

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/MFXYIVRTHJGNCYBN6BLE7MXU4L \
  | 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: 616f8456333a4cd1602df0564fb2f4e2f6cf781cf826ba7a71647182765fbbf4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "500a03f642f36c77bc8581c441b4e43f0cc8f4d2f977d3cefb16b4d16cda2f9f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-01-10T16:01:29Z",
    "title_canon_sha256": "6fc6bc6dfebc6d74e6244533744e3bff1454965ec105430541b5f07acc0e7f56"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.1855",
    "kind": "arxiv",
    "version": 1
  }
}