Pith Number

pith:DQ32MAZ5

pith:2026:DQ32MAZ5KYBOR3UOLGQFNFB6E6

not attested not anchored not stored refs pending

Path-Dependent Ergodic Optimal Control and Backward Stochastic Differential Equations

Mathieu Lise, Nizar Touzi, Xuyang Lin

arxiv:2606.06757 v1 · 2026-06-04 · math.PR · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DQ32MAZ5KYBOR3UOLGQFNFB6E6}

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	2026-06-08T01:04:26.799769Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1c37a6033d5602e8ee8e59a056943e27ac7115d8ea000b0d78169a3aea6e6e1c

Aliases

arxiv: 2606.06757 · arxiv_version: 2606.06757v1 · doi: 10.48550/arxiv.2606.06757 · pith_short_12: DQ32MAZ5KYBO · pith_short_16: DQ32MAZ5KYBOR3UO · pith_short_8: DQ32MAZ5

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/DQ32MAZ5KYBOR3UOLGQFNFB6E6 \
  | 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: 1c37a6033d5602e8ee8e59a056943e27ac7115d8ea000b0d78169a3aea6e6e1c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "62670401d3cd8e54fa181d33586f4ff68392dd22d3a148fd88d0f6181d2ae15c",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-04T22:39:17Z",
    "title_canon_sha256": "6d3313cd8c5841925ba43873489122d1b48d9fc3e90349dc6c1fb485511f66be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.06757",
    "kind": "arxiv",
    "version": 1
  }
}