{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:XX4QL6ZZR4VCROYDGIUE2DODAP","short_pith_number":"pith:XX4QL6ZZ","canonical_record":{"source":{"id":"1310.7825","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-10-29T15:08:41Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"70249fd3e6f6de8ac9d1f478348e38b4430eb8196d928a8a3d36e0d55af20d0b","abstract_canon_sha256":"99f26bbf155d6b16562f75bf78ec098ca2ff0e797758e285aec22ad2a006c140"},"schema_version":"1.0"},"canonical_sha256":"bdf905fb398f2a28bb0332284d0dc303c68aa8b4e625345bde87df2f73bb6d01","source":{"kind":"arxiv","id":"1310.7825","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7825","created_at":"2026-05-18T01:46:47Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7825v2","created_at":"2026-05-18T01:46:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7825","created_at":"2026-05-18T01:46:47Z"},{"alias_kind":"pith_short_12","alias_value":"XX4QL6ZZR4VC","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XX4QL6ZZR4VCROYD","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XX4QL6ZZ","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:XX4QL6ZZR4VCROYDGIUE2DODAP","target":"record","payload":{"canonical_record":{"source":{"id":"1310.7825","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-10-29T15:08:41Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"70249fd3e6f6de8ac9d1f478348e38b4430eb8196d928a8a3d36e0d55af20d0b","abstract_canon_sha256":"99f26bbf155d6b16562f75bf78ec098ca2ff0e797758e285aec22ad2a006c140"},"schema_version":"1.0"},"canonical_sha256":"bdf905fb398f2a28bb0332284d0dc303c68aa8b4e625345bde87df2f73bb6d01","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:46:47.876178Z","signature_b64":"kT4tM37n7MYpwayBj42+xst4uj9fGsmC9PLgINNpEzlXrZSFCwPxau7pqHBKDK4rcfjvysbbOm6NoF0uTQfZDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bdf905fb398f2a28bb0332284d0dc303c68aa8b4e625345bde87df2f73bb6d01","last_reissued_at":"2026-05-18T01:46:47.875620Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:46:47.875620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.7825","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":"2026-05-18T01:46:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qFGnlXzp3PkrnaQsWFjQn47SnBx/BC0jOg+v8BKGt9g91YxKd7mzMsD797iHX/FhEcXIhVp1h2EEfhqe81D+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:20:03.264135Z"},"content_sha256":"be2891bd9f08a3cb26c13eb8401ce52390f2e34b17d3943f4dc55ec422e62650","schema_version":"1.0","event_id":"sha256:be2891bd9f08a3cb26c13eb8401ce52390f2e34b17d3943f4dc55ec422e62650"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:XX4QL6ZZR4VCROYDGIUE2DODAP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantifying Networks Complexity from Information Geometry Viewpoint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Domenico Felice, Marco Pettini, Stefano Mancini","submitted_at":"2013-10-29T15:08:41Z","abstract_excerpt":"We consider a Gaussian statistical model whose parameter space is given by the variances of random variables. Underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as weighted edges among vertices. We then associate to the parameter space a statistical manifold endowed with a Riemannian metric structure (that of Fisher-Rao). Going on, in analogy with the microcanonical definition of entropy in Statistical Mechanics, we introduce an entropic measure of networks complexity. We prove that it is invariant under networks isomorphis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7825","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":"2026-05-18T01:46:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6ijHabCI4sDmS0KI45eXyuia1HhsyvyG1hrOqskUjJazqZhWJl4Mg7qLLxm2DzjRGR7F+CkvvTKfolVfEVASBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:20:03.264504Z"},"content_sha256":"f1ea1d4bf3a768c72bfccee7821ccabb0b77b2631d7c698a1465bef74f945428","schema_version":"1.0","event_id":"sha256:f1ea1d4bf3a768c72bfccee7821ccabb0b77b2631d7c698a1465bef74f945428"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XX4QL6ZZR4VCROYDGIUE2DODAP/bundle.json","state_url":"https://pith.science/pith/XX4QL6ZZR4VCROYDGIUE2DODAP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XX4QL6ZZR4VCROYDGIUE2DODAP/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":"2026-05-28T06:20:03Z","links":{"resolver":"https://pith.science/pith/XX4QL6ZZR4VCROYDGIUE2DODAP","bundle":"https://pith.science/pith/XX4QL6ZZR4VCROYDGIUE2DODAP/bundle.json","state":"https://pith.science/pith/XX4QL6ZZR4VCROYDGIUE2DODAP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XX4QL6ZZR4VCROYDGIUE2DODAP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XX4QL6ZZR4VCROYDGIUE2DODAP","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":"99f26bbf155d6b16562f75bf78ec098ca2ff0e797758e285aec22ad2a006c140","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-10-29T15:08:41Z","title_canon_sha256":"70249fd3e6f6de8ac9d1f478348e38b4430eb8196d928a8a3d36e0d55af20d0b"},"schema_version":"1.0","source":{"id":"1310.7825","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7825","created_at":"2026-05-18T01:46:47Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7825v2","created_at":"2026-05-18T01:46:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7825","created_at":"2026-05-18T01:46:47Z"},{"alias_kind":"pith_short_12","alias_value":"XX4QL6ZZR4VC","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XX4QL6ZZR4VCROYD","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XX4QL6ZZ","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:f1ea1d4bf3a768c72bfccee7821ccabb0b77b2631d7c698a1465bef74f945428","target":"graph","created_at":"2026-05-18T01:46:47Z","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 consider a Gaussian statistical model whose parameter space is given by the variances of random variables. Underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as weighted edges among vertices. We then associate to the parameter space a statistical manifold endowed with a Riemannian metric structure (that of Fisher-Rao). Going on, in analogy with the microcanonical definition of entropy in Statistical Mechanics, we introduce an entropic measure of networks complexity. We prove that it is invariant under networks isomorphis","authors_text":"Domenico Felice, Marco Pettini, Stefano Mancini","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-10-29T15:08:41Z","title":"Quantifying Networks Complexity from Information Geometry Viewpoint"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7825","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:be2891bd9f08a3cb26c13eb8401ce52390f2e34b17d3943f4dc55ec422e62650","target":"record","created_at":"2026-05-18T01:46:47Z","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":"99f26bbf155d6b16562f75bf78ec098ca2ff0e797758e285aec22ad2a006c140","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-10-29T15:08:41Z","title_canon_sha256":"70249fd3e6f6de8ac9d1f478348e38b4430eb8196d928a8a3d36e0d55af20d0b"},"schema_version":"1.0","source":{"id":"1310.7825","kind":"arxiv","version":2}},"canonical_sha256":"bdf905fb398f2a28bb0332284d0dc303c68aa8b4e625345bde87df2f73bb6d01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bdf905fb398f2a28bb0332284d0dc303c68aa8b4e625345bde87df2f73bb6d01","first_computed_at":"2026-05-18T01:46:47.875620Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:46:47.875620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kT4tM37n7MYpwayBj42+xst4uj9fGsmC9PLgINNpEzlXrZSFCwPxau7pqHBKDK4rcfjvysbbOm6NoF0uTQfZDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:46:47.876178Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7825","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be2891bd9f08a3cb26c13eb8401ce52390f2e34b17d3943f4dc55ec422e62650","sha256:f1ea1d4bf3a768c72bfccee7821ccabb0b77b2631d7c698a1465bef74f945428"],"state_sha256":"a4c807c80cdf4c4987245f577109cf3f6e38acd904a8a1dc5cd91934c7702a25"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MZMfgZzdXL20jaPCH20ywxVsUqc7KbTBQZnbdFgfowT9+xoBbgoYW5Qw02oDFxM4j2/ieXa1Sxi2UBe81lIYDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T06:20:03.266658Z","bundle_sha256":"3150a0a7c6c06dcf1a72ab7db41a7115d2ec01b4a871dc7653ec7453c7fbc8d1"}}