Pith Number

pith:Q54HKMNI

pith:1999:Q54HKMNIMGTFL3YYD6X7M5HU2T

not attested not anchored not stored refs pending

Aubry-Mather theory and idempotent eigenfunctions of the Bellman operator

Andrei Sobolevskii

arxiv:chao-dyn/9906036 v2 · 1999-06-23 · chao-dyn · math.DS · nlin.CD

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q54HKMNIMGTFL3YYD6X7M5HU2T}

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	2026-05-18T01:07:24.479448Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87787531a861a655ef181faff674f4d4d4329d7a570fd12a18c55785b0c14e8c

Aliases

arxiv: chao-dyn/9906036 · arxiv_version: chao-dyn/9906036v2 · doi: 10.48550/arxiv.chao-dyn/9906036 · pith_short_12: Q54HKMNIMGTF · pith_short_16: Q54HKMNIMGTFL3YY · pith_short_8: Q54HKMNI

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/Q54HKMNIMGTFL3YYD6X7M5HU2T \
  | 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: 87787531a861a655ef181faff674f4d4d4329d7a570fd12a18c55785b0c14e8c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "941310806ad5a95cb790edd9ec615c66728353aff338f118b9e239e0aaedb822",
    "cross_cats_sorted": [
      "math.DS",
      "nlin.CD"
    ],
    "license": "",
    "primary_cat": "chao-dyn",
    "submitted_at": "1999-06-23T09:19:22Z",
    "title_canon_sha256": "63e68a6a3e6ea1e19d8fed9d2a3a8a8e5462d7286e8fad822229f864e9d56b7e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "chao-dyn/9906036",
    "kind": "arxiv",
    "version": 2
  }
}