Pith Number

pith:ODMXM2YJ

pith:2020:ODMXM2YJY4P5RCYJMM7LCA33MU

not attested not anchored not stored refs pending

Hyperbolic Concentration, Anti-concentration, and Discrepancy

Ruizhe Zhang, Zhao Song

arxiv:2008.09593 v3 · 2020-08-21 · math.PR · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ODMXM2YJY4P5RCYJMM7LCA33MU}

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	2026-07-05T04:40:06.227759Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

70d9766b09c71fd88b09633eb1037b653519ddf1e6fa3f97ced27e30ecbe16cc

Aliases

arxiv: 2008.09593 · arxiv_version: 2008.09593v3 · doi: 10.48550/arxiv.2008.09593 · pith_short_12: ODMXM2YJY4P5 · pith_short_16: ODMXM2YJY4P5RCYJ · pith_short_8: ODMXM2YJ

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/ODMXM2YJY4P5RCYJMM7LCA33MU \
  | 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: 70d9766b09c71fd88b09633eb1037b653519ddf1e6fa3f97ced27e30ecbe16cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e6aa8ca4a299a15bfa76f13eb385cf61252d83c6f65a7f630f8dd02fa1e4c5c8",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2020-08-21T17:39:52Z",
    "title_canon_sha256": "183d9db0a0fca6e202882a9321ac28cf45c699c28c0e49c5c37db4527f9838f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2008.09593",
    "kind": "arxiv",
    "version": 3
  }
}