Pith Number

pith:TWVV5G56

pith:2011:TWVV5G56DDQQ4C6TXXRHVMZIA5

not attested not anchored not stored refs pending

Mod-$\phi$ convergence

Ashkan Nikeghbali, Emmanuel Kowalski, Freddy Delbaen

arxiv:1107.5657 v2 · 2011-07-28 · math.PR · 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{TWVV5G56DDQQ4C6TXXRHVMZIA5}

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	2026-05-18T04:16:40.501095Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9dab5e9bbe18e10e0bd3bde27ab328074600bf2910038142921378f487b812c7

Aliases

arxiv: 1107.5657 · arxiv_version: 1107.5657v2 · doi: 10.48550/arxiv.1107.5657 · pith_short_12: TWVV5G56DDQQ · pith_short_16: TWVV5G56DDQQ4C6T · pith_short_8: TWVV5G56

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/TWVV5G56DDQQ4C6TXXRHVMZIA5 \
  | 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: 9dab5e9bbe18e10e0bd3bde27ab328074600bf2910038142921378f487b812c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c96d5f7160838b0dc99c3f0b98ca9e9f3897ef088bd3cfd0720321546ef88a72",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-07-28T09:33:04Z",
    "title_canon_sha256": "0d24c71e8750a12e7c35994104e0e015a839b7dede1e43aae53cc8234e063186"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.5657",
    "kind": "arxiv",
    "version": 2
  }
}