Pith Number

pith:X6NT3ZFK

pith:2026:X6NT3ZFKOQGQD4SYRN45E6NI7S

not attested not anchored not stored refs pending

Perturbed utility Markovian traffic equilibrium: theory and computation

Kenan Zhang, Rui Yao

arxiv:2607.09568 v1 · 2026-07-10 · math.OC · econ.GN · econ.TH · q-fin.EC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X6NT3ZFKOQGQD4SYRN45E6NI7S}

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	2026-07-13T01:20:20.691082Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf9b3de4aa740d01f2588b79d279a8fc82b1485df318e87d34aec4492f97bce1

Aliases

arxiv: 2607.09568 · arxiv_version: 2607.09568v1 · doi: 10.48550/arxiv.2607.09568 · pith_short_12: X6NT3ZFKOQGQ · pith_short_16: X6NT3ZFKOQGQD4SY · pith_short_8: X6NT3ZFK

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/X6NT3ZFKOQGQD4SYRN45E6NI7S \
  | 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: bf9b3de4aa740d01f2588b79d279a8fc82b1485df318e87d34aec4492f97bce1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0aa5fc84b40161653f872405f0d02ea9c36935d187d3d09be722a0d5b9748aa8",
    "cross_cats_sorted": [
      "econ.GN",
      "econ.TH",
      "q-fin.EC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-07-10T16:15:12Z",
    "title_canon_sha256": "39d6ebf4112c03e8e82d16b325b4c15e0a7a3b1f79bea1cb80f6520892188d1e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.09568",
    "kind": "arxiv",
    "version": 1
  }
}