{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:WFXY4JY5NK5AX6WSMTHR23NYAQ","short_pith_number":"pith:WFXY4JY5","canonical_record":{"source":{"id":"0710.3972","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2007-10-22T04:54:01Z","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph"],"title_canon_sha256":"bb1a5d7640c672134cfaf8cc6c63830f133012d08e81611c06216afa70f1afff","abstract_canon_sha256":"6628a6b5e1d447836f4a2cb5c17f6a4fb6073b098bedcda7c44abaeab72e9551"},"schema_version":"1.0"},"canonical_sha256":"b16f8e271d6aba0bfad264cf1d6db80433c8a8ff02aafce248416aa3b59ba6ba","source":{"kind":"arxiv","id":"0710.3972","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.3972","created_at":"2026-05-18T03:13:11Z"},{"alias_kind":"arxiv_version","alias_value":"0710.3972v3","created_at":"2026-05-18T03:13:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.3972","created_at":"2026-05-18T03:13:11Z"},{"alias_kind":"pith_short_12","alias_value":"WFXY4JY5NK5A","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"WFXY4JY5NK5AX6WS","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"WFXY4JY5","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:WFXY4JY5NK5AX6WSMTHR23NYAQ","target":"record","payload":{"canonical_record":{"source":{"id":"0710.3972","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2007-10-22T04:54:01Z","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph"],"title_canon_sha256":"bb1a5d7640c672134cfaf8cc6c63830f133012d08e81611c06216afa70f1afff","abstract_canon_sha256":"6628a6b5e1d447836f4a2cb5c17f6a4fb6073b098bedcda7c44abaeab72e9551"},"schema_version":"1.0"},"canonical_sha256":"b16f8e271d6aba0bfad264cf1d6db80433c8a8ff02aafce248416aa3b59ba6ba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:11.291244Z","signature_b64":"r5tLuTghWrqLUqg7jim5DzkeC7bz+K8CtgIHjXsq0B1tgQB10eKQ9FsXCWJLgdPTheNHsx62obtDZ89J/Cv3AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b16f8e271d6aba0bfad264cf1d6db80433c8a8ff02aafce248416aa3b59ba6ba","last_reissued_at":"2026-05-18T03:13:11.290467Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:11.290467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0710.3972","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:13:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hwez0Xh6GNFB1KX+m0+4GVrB4yDzdSAi79pe22TCHXxM3AzVgjhMyCJuXvo+nNkI8o32253jcN3ljZPfF0vpDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T17:54:43.744404Z"},"content_sha256":"089900523e4d720c47b97f246476f47b2ff6011508f6a6619abd28d4ce4c8592","schema_version":"1.0","event_id":"sha256:089900523e4d720c47b97f246476f47b2ff6011508f6a6619abd28d4ce4c8592"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:WFXY4JY5NK5AX6WSMTHR23NYAQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Centrality measures and thermodynamic formalism for complex networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","physics.soc-ph"],"primary_cat":"physics.data-an","authors_text":"Anne-Sophie Libert, Jean-Charles Delvenne","submitted_at":"2007-10-22T04:54:01Z","abstract_excerpt":"In the study of small and large networks it is customary to perform a simple random walk, where the random walker jumps from one node to one of its neighbours with uniform probability. The properties of this random walk are intimately related to the combinatorial properties of the network. In this paper we propose to use the Ruelle-Bowens random walk instead, whose probability transitions are chosen in order to maximise the entropy rate of the walk on an unweighted graph. If the graph is weighted, then a free energy is optimised instead of entropy rate.\n  Specifically, we introduce a centralit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.3972","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:13:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+yy4mCXZhnjc1I08FpC0thHSWMWUTra3CDCvtAh06sU1TENZN3jQ+JW+X8rHnFMhHSVjWAKTYdC4g+hP4ECbAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T17:54:43.744743Z"},"content_sha256":"e93ab55489eca7ce577838616396414bc58629fba52d71c497542e6d24a6ba99","schema_version":"1.0","event_id":"sha256:e93ab55489eca7ce577838616396414bc58629fba52d71c497542e6d24a6ba99"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WFXY4JY5NK5AX6WSMTHR23NYAQ/bundle.json","state_url":"https://pith.science/pith/WFXY4JY5NK5AX6WSMTHR23NYAQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WFXY4JY5NK5AX6WSMTHR23NYAQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T17:54:43Z","links":{"resolver":"https://pith.science/pith/WFXY4JY5NK5AX6WSMTHR23NYAQ","bundle":"https://pith.science/pith/WFXY4JY5NK5AX6WSMTHR23NYAQ/bundle.json","state":"https://pith.science/pith/WFXY4JY5NK5AX6WSMTHR23NYAQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WFXY4JY5NK5AX6WSMTHR23NYAQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:WFXY4JY5NK5AX6WSMTHR23NYAQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6628a6b5e1d447836f4a2cb5c17f6a4fb6073b098bedcda7c44abaeab72e9551","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2007-10-22T04:54:01Z","title_canon_sha256":"bb1a5d7640c672134cfaf8cc6c63830f133012d08e81611c06216afa70f1afff"},"schema_version":"1.0","source":{"id":"0710.3972","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.3972","created_at":"2026-05-18T03:13:11Z"},{"alias_kind":"arxiv_version","alias_value":"0710.3972v3","created_at":"2026-05-18T03:13:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.3972","created_at":"2026-05-18T03:13:11Z"},{"alias_kind":"pith_short_12","alias_value":"WFXY4JY5NK5A","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"WFXY4JY5NK5AX6WS","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"WFXY4JY5","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:e93ab55489eca7ce577838616396414bc58629fba52d71c497542e6d24a6ba99","target":"graph","created_at":"2026-05-18T03:13:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In the study of small and large networks it is customary to perform a simple random walk, where the random walker jumps from one node to one of its neighbours with uniform probability. The properties of this random walk are intimately related to the combinatorial properties of the network. In this paper we propose to use the Ruelle-Bowens random walk instead, whose probability transitions are chosen in order to maximise the entropy rate of the walk on an unweighted graph. If the graph is weighted, then a free energy is optimised instead of entropy rate.\n  Specifically, we introduce a centralit","authors_text":"Anne-Sophie Libert, Jean-Charles Delvenne","cross_cats":["cond-mat.stat-mech","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2007-10-22T04:54:01Z","title":"Centrality measures and thermodynamic formalism for complex networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.3972","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:089900523e4d720c47b97f246476f47b2ff6011508f6a6619abd28d4ce4c8592","target":"record","created_at":"2026-05-18T03:13:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6628a6b5e1d447836f4a2cb5c17f6a4fb6073b098bedcda7c44abaeab72e9551","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2007-10-22T04:54:01Z","title_canon_sha256":"bb1a5d7640c672134cfaf8cc6c63830f133012d08e81611c06216afa70f1afff"},"schema_version":"1.0","source":{"id":"0710.3972","kind":"arxiv","version":3}},"canonical_sha256":"b16f8e271d6aba0bfad264cf1d6db80433c8a8ff02aafce248416aa3b59ba6ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b16f8e271d6aba0bfad264cf1d6db80433c8a8ff02aafce248416aa3b59ba6ba","first_computed_at":"2026-05-18T03:13:11.290467Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:11.290467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r5tLuTghWrqLUqg7jim5DzkeC7bz+K8CtgIHjXsq0B1tgQB10eKQ9FsXCWJLgdPTheNHsx62obtDZ89J/Cv3AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:11.291244Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.3972","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:089900523e4d720c47b97f246476f47b2ff6011508f6a6619abd28d4ce4c8592","sha256:e93ab55489eca7ce577838616396414bc58629fba52d71c497542e6d24a6ba99"],"state_sha256":"e13cd39ca70a5b417a2fe361e11563f1643b6db21ef675bf7d6832e62bbb5e34"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7VhwbOTu0yB64wAvqJaMA3Ydxjo35maIvZ3+h5hPTG+bC2LNk7zUZ+QHeOwc/oPUK+O7NnEy42qHZLTHrLnMBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T17:54:43.746640Z","bundle_sha256":"80b659437de6b0ceff3080bb77c311626c14f8975fe61ef49f6cbf1cd95a009a"}}