Pith Number

pith:GVYXYDNK

pith:2020:GVYXYDNK7MIPNC2TK2HUJZRKHV

not attested not anchored not stored refs pending

Missing Mass Concentration for Markov Chains

Maciej Skorski

arxiv:2001.03603 v2 · 2020-01-10 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GVYXYDNK7MIPNC2TK2HUJZRKHV}

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	2026-07-05T00:33:26.261223Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35717c0daafb10f68b53568f44e62a3d77aa6c9fda570afcc3fa0f13a7e78f20

Aliases

arxiv: 2001.03603 · arxiv_version: 2001.03603v2 · doi: 10.48550/arxiv.2001.03603 · pith_short_12: GVYXYDNK7MIP · pith_short_16: GVYXYDNK7MIPNC2T · pith_short_8: GVYXYDNK

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/GVYXYDNK7MIPNC2TK2HUJZRKHV \
  | 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: 35717c0daafb10f68b53568f44e62a3d77aa6c9fda570afcc3fa0f13a7e78f20

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0627cc1b670a4fd42aa3543bc41ecbc6f597b07a8811fb9a15a4f8ea4ea8e2ff",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2020-01-10T18:36:08Z",
    "title_canon_sha256": "c7b6d053cbf59a7174540abb5fdb9cef9efd19b6574c55cbd3f847f39a72e857"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2001.03603",
    "kind": "arxiv",
    "version": 2
  }
}