{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:HII2JDC4ANXYZTPETRQFR6SXFM","short_pith_number":"pith:HII2JDC4","canonical_record":{"source":{"id":"0812.2597","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2008-12-14T05:23:10Z","cross_cats_sorted":["q-bio.MN","quant-ph"],"title_canon_sha256":"11083126bf120101f4de65bbe14b969b7e6b6725ebbbe1b504c850e88550051a","abstract_canon_sha256":"dd328e090baaa822e2c5826ec6cd07a014810f3cc6d7352af00c299665468159"},"schema_version":"1.0"},"canonical_sha256":"3a11a48c5c036f8ccde49c6058fa572b12b4202a2a7ed17be1a30250f35fbdc6","source":{"kind":"arxiv","id":"0812.2597","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.2597","created_at":"2026-05-18T03:57:25Z"},{"alias_kind":"arxiv_version","alias_value":"0812.2597v2","created_at":"2026-05-18T03:57:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.2597","created_at":"2026-05-18T03:57:25Z"},{"alias_kind":"pith_short_12","alias_value":"HII2JDC4ANXY","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"HII2JDC4ANXYZTPE","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"HII2JDC4","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:HII2JDC4ANXYZTPETRQFR6SXFM","target":"record","payload":{"canonical_record":{"source":{"id":"0812.2597","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2008-12-14T05:23:10Z","cross_cats_sorted":["q-bio.MN","quant-ph"],"title_canon_sha256":"11083126bf120101f4de65bbe14b969b7e6b6725ebbbe1b504c850e88550051a","abstract_canon_sha256":"dd328e090baaa822e2c5826ec6cd07a014810f3cc6d7352af00c299665468159"},"schema_version":"1.0"},"canonical_sha256":"3a11a48c5c036f8ccde49c6058fa572b12b4202a2a7ed17be1a30250f35fbdc6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:25.530758Z","signature_b64":"QSFWBT/MAFh9+HcAOzGMMXVLhKKl05eHWhIF43mrKY/NV5Uvk0+OMZDpAsJNHOqnbhaOLDz0w3Tv1FHDIv6yDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a11a48c5c036f8ccde49c6058fa572b12b4202a2a7ed17be1a30250f35fbdc6","last_reissued_at":"2026-05-18T03:57:25.530134Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:25.530134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0812.2597","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:57:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KxYxYU08Bk74A8W5RDaURyxFgHPgWSL4oaMWv7OK2s2TiveSbjaQ111bT3MXqNWI2ygOBy/FI1wnyt+kI+nVAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T18:01:04.798391Z"},"content_sha256":"03eb44f2c63e0be66a017c2da19b82be10666359f2d5ad9af65fae333a22ab18","schema_version":"1.0","event_id":"sha256:03eb44f2c63e0be66a017c2da19b82be10666359f2d5ad9af65fae333a22ab18"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:HII2JDC4ANXYZTPETRQFR6SXFM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The von Neumann entropy of networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.MN","quant-ph"],"primary_cat":"cond-mat.dis-nn","authors_text":"Filippo Passerini, Simone Severini","submitted_at":"2008-12-14T05:23:10Z","abstract_excerpt":"We normalize the combinatorial Laplacian of a graph by the degree sum, look at its eigenvalues as a probability distribution and then study its Shannon entropy. Equivalently, we represent a graph with a quantum mechanical state and study its von Neumann entropy. At the graph-theoretic level, this quantity may be interpreted as a measure of regularity; it tends to be larger in relation to the number of connected components, long paths and nontrivial symmetries. When the set of vertices is asymptotically large, we prove that regular graphs and the complete graph have equal entropy, and specifica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.2597","kind":"arxiv","version":2},"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":"2026-05-18T03:57:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UfEwMq64BU46KLA4IGFS/6KXh0PEu18o8znv5A8xTPUNBYYNS8j7z8zsxKUDIzyiB7UzL3E499vkJgIhiNQOCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T18:01:04.798823Z"},"content_sha256":"26a3d6b5b7c9ee2e2192d0de5c8f339f70ea07951f2606fd75ee03a88cb174ff","schema_version":"1.0","event_id":"sha256:26a3d6b5b7c9ee2e2192d0de5c8f339f70ea07951f2606fd75ee03a88cb174ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HII2JDC4ANXYZTPETRQFR6SXFM/bundle.json","state_url":"https://pith.science/pith/HII2JDC4ANXYZTPETRQFR6SXFM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HII2JDC4ANXYZTPETRQFR6SXFM/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":"2026-05-20T18:01:04Z","links":{"resolver":"https://pith.science/pith/HII2JDC4ANXYZTPETRQFR6SXFM","bundle":"https://pith.science/pith/HII2JDC4ANXYZTPETRQFR6SXFM/bundle.json","state":"https://pith.science/pith/HII2JDC4ANXYZTPETRQFR6SXFM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HII2JDC4ANXYZTPETRQFR6SXFM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:HII2JDC4ANXYZTPETRQFR6SXFM","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":"dd328e090baaa822e2c5826ec6cd07a014810f3cc6d7352af00c299665468159","cross_cats_sorted":["q-bio.MN","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2008-12-14T05:23:10Z","title_canon_sha256":"11083126bf120101f4de65bbe14b969b7e6b6725ebbbe1b504c850e88550051a"},"schema_version":"1.0","source":{"id":"0812.2597","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.2597","created_at":"2026-05-18T03:57:25Z"},{"alias_kind":"arxiv_version","alias_value":"0812.2597v2","created_at":"2026-05-18T03:57:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.2597","created_at":"2026-05-18T03:57:25Z"},{"alias_kind":"pith_short_12","alias_value":"HII2JDC4ANXY","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"HII2JDC4ANXYZTPE","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"HII2JDC4","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:26a3d6b5b7c9ee2e2192d0de5c8f339f70ea07951f2606fd75ee03a88cb174ff","target":"graph","created_at":"2026-05-18T03:57:25Z","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":"We normalize the combinatorial Laplacian of a graph by the degree sum, look at its eigenvalues as a probability distribution and then study its Shannon entropy. Equivalently, we represent a graph with a quantum mechanical state and study its von Neumann entropy. At the graph-theoretic level, this quantity may be interpreted as a measure of regularity; it tends to be larger in relation to the number of connected components, long paths and nontrivial symmetries. When the set of vertices is asymptotically large, we prove that regular graphs and the complete graph have equal entropy, and specifica","authors_text":"Filippo Passerini, Simone Severini","cross_cats":["q-bio.MN","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2008-12-14T05:23:10Z","title":"The von Neumann entropy of networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.2597","kind":"arxiv","version":2},"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":"sha256:03eb44f2c63e0be66a017c2da19b82be10666359f2d5ad9af65fae333a22ab18","target":"record","created_at":"2026-05-18T03:57:25Z","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":"dd328e090baaa822e2c5826ec6cd07a014810f3cc6d7352af00c299665468159","cross_cats_sorted":["q-bio.MN","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2008-12-14T05:23:10Z","title_canon_sha256":"11083126bf120101f4de65bbe14b969b7e6b6725ebbbe1b504c850e88550051a"},"schema_version":"1.0","source":{"id":"0812.2597","kind":"arxiv","version":2}},"canonical_sha256":"3a11a48c5c036f8ccde49c6058fa572b12b4202a2a7ed17be1a30250f35fbdc6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a11a48c5c036f8ccde49c6058fa572b12b4202a2a7ed17be1a30250f35fbdc6","first_computed_at":"2026-05-18T03:57:25.530134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:25.530134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QSFWBT/MAFh9+HcAOzGMMXVLhKKl05eHWhIF43mrKY/NV5Uvk0+OMZDpAsJNHOqnbhaOLDz0w3Tv1FHDIv6yDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:25.530758Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.2597","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03eb44f2c63e0be66a017c2da19b82be10666359f2d5ad9af65fae333a22ab18","sha256:26a3d6b5b7c9ee2e2192d0de5c8f339f70ea07951f2606fd75ee03a88cb174ff"],"state_sha256":"f7c452a5cc52a37a642539e28aac660166dac8d44329d5c393906158cb5da5bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8j9k6GxRy+yZSPbf/Umd2FJaFd2mFRo7YnU2XicisYgiY5Hqz1i7tB+GyqzUjZrDT+hAfjTQ7kRASy2enUamCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T18:01:04.801225Z","bundle_sha256":"3bebdddba456d389f1130e4b5627404ba49b804956d8c5d629028f2f247213eb"}}