Pith Number

pith:NZT4DV27

pith:2016:NZT4DV27UHATUIY2VZVM7F2SFR

not attested not anchored not stored refs pending

A necessary and sufficient condition for a matrix equilibrium state to be mixing

Ian D. Morris

arxiv:1612.01761 v1 · 2016-12-06 · 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{NZT4DV27UHATUIY2VZVM7F2SFR}

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	2026-05-18T00:55:47.662557Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6e67c1d75fa1c13a231aae6acf97522c6dba1e89299edc39670daef311eb28a8

Aliases

arxiv: 1612.01761 · arxiv_version: 1612.01761v1 · doi: 10.48550/arxiv.1612.01761 · pith_short_12: NZT4DV27UHAT · pith_short_16: NZT4DV27UHATUIY2 · pith_short_8: NZT4DV27

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/NZT4DV27UHATUIY2VZVM7F2SFR \
  | 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: 6e67c1d75fa1c13a231aae6acf97522c6dba1e89299edc39670daef311eb28a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a89b4e8ddea5c56683761986d5f36701867be0ea68ebf21035a7f9697626c76d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-12-06T11:27:28Z",
    "title_canon_sha256": "979bae1b465acf84c4cdca0032976d255919e384325a4fa69b83dcf7598b82f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.01761",
    "kind": "arxiv",
    "version": 1
  }
}