Pith Number

pith:BBGPN4SX

pith:2025:BBGPN4SXCDA2FRWZC2HH22WMQN

not attested not anchored not stored refs pending

Thermodynamics and Legendre Duality in Optimal Networks

Amilcare Porporato, Lamberto Rondoni, Luca Ridolfi, Salvatore Calabrese, Shashank Kumar Anand

arxiv:2506.15727 v1 · 2025-06-09 · cond-mat.stat-mech · nlin.AO · physics.app-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BBGPN4SXCDA2FRWZC2HH22WMQN}

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	2026-07-05T11:23:51.275860Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

084cf6f25710c1a2c6d9168e7d6acc8379f3348e17e06b893cc91ec8f215cf58

Aliases

arxiv: 2506.15727 · arxiv_version: 2506.15727v1 · doi: 10.48550/arxiv.2506.15727 · pith_short_12: BBGPN4SXCDA2 · pith_short_16: BBGPN4SXCDA2FRWZ · pith_short_8: BBGPN4SX

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/BBGPN4SXCDA2FRWZC2HH22WMQN \
  | 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: 084cf6f25710c1a2c6d9168e7d6acc8379f3348e17e06b893cc91ec8f215cf58

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f97bf728819382681c7dfd1f2293c9bf43a6c5a211ea7039eadf13760ce0cbed",
    "cross_cats_sorted": [
      "nlin.AO",
      "physics.app-ph"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2025-06-09T16:51:33Z",
    "title_canon_sha256": "89b005a48eae5d64bd98f3858f7298a4927f299c27b8d6d5f760145c70bf1499"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.15727",
    "kind": "arxiv",
    "version": 1
  }
}