{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:GKUWJDQC6UTGJ5HUTAKVWSSKX6","short_pith_number":"pith:GKUWJDQC","canonical_record":{"source":{"id":"1511.07248","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-11-23T14:51:52Z","cross_cats_sorted":[],"title_canon_sha256":"93c1fa99f42787bff6e1da122e5df049ce429fea0457d01dc8817eeac25eeeb6","abstract_canon_sha256":"acb4cb7c7b83e5623ad67820088cdf10fdd875396b34f16e71a662a826a184e1"},"schema_version":"1.0"},"canonical_sha256":"32a9648e02f52664f4f498155b4a4abfa339a10d0f15be557ee8058b08b8dacd","source":{"kind":"arxiv","id":"1511.07248","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.07248","created_at":"2026-05-18T01:20:29Z"},{"alias_kind":"arxiv_version","alias_value":"1511.07248v1","created_at":"2026-05-18T01:20:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07248","created_at":"2026-05-18T01:20:29Z"},{"alias_kind":"pith_short_12","alias_value":"GKUWJDQC6UTG","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GKUWJDQC6UTGJ5HU","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GKUWJDQC","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:GKUWJDQC6UTGJ5HUTAKVWSSKX6","target":"record","payload":{"canonical_record":{"source":{"id":"1511.07248","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-11-23T14:51:52Z","cross_cats_sorted":[],"title_canon_sha256":"93c1fa99f42787bff6e1da122e5df049ce429fea0457d01dc8817eeac25eeeb6","abstract_canon_sha256":"acb4cb7c7b83e5623ad67820088cdf10fdd875396b34f16e71a662a826a184e1"},"schema_version":"1.0"},"canonical_sha256":"32a9648e02f52664f4f498155b4a4abfa339a10d0f15be557ee8058b08b8dacd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:29.083249Z","signature_b64":"tQ0Da06FhPqx/RxmC/K9ToSZIHtEHxVXMZuGdMzbgstfixWI8SOaM1Iu5sld4tc9fsfIf+etTRnFBG7UW/1yBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32a9648e02f52664f4f498155b4a4abfa339a10d0f15be557ee8058b08b8dacd","last_reissued_at":"2026-05-18T01:20:29.082645Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:29.082645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.07248","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T8sbHaZFP/f1W6a2q6DpFSKM3QFj8tOE7lIaK3QyrVRSuu4E9gdt6dKt3NeZ3HBnoLIU/uWaioRTa3lPDEBjBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:03:59.610106Z"},"content_sha256":"97f9e3a15a8707ab9ad17f141438cffdf3d4ba1dc64cc5606d4db870b72e606e","schema_version":"1.0","event_id":"sha256:97f9e3a15a8707ab9ad17f141438cffdf3d4ba1dc64cc5606d4db870b72e606e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:GKUWJDQC6UTGJ5HUTAKVWSSKX6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multifractal analysis of weighted networks by a modified sandbox algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.soc-ph","authors_text":"Bao-Gen Li, Jin-Long Liu, Yu-Qin Song, Zu-Guo Yu","submitted_at":"2015-11-23T14:51:52Z","abstract_excerpt":"Complex networks have attracted growing attention in many fields. As a generalization of fractal analysis, multifractal analysis (MFA) is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. Some algorithms for MFA of unweighted complex networks have been proposed in the past a few years, including the sandbox (SB) algorithm recently employed by our group. In this paper, a modified SB algorithm (we call it SBw algorithm) is proposed for MFA of weighted networks.First, we use the SBw algorithm to study the multifractal property"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07248","kind":"arxiv","version":1},"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":"2026-05-18T01:20:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"97Huo3edR6sk3ReWvpvjiA8EUxQ9DLsLEYAv5buc3aBNV0Wtrb86LvNunqzk2vTrSib82E01rtoMMGxp8utaBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:03:59.610833Z"},"content_sha256":"42f06aa41d6095f8eb3531667ccdf0262546a8cc1c06d06a40ffa02a2170a0bb","schema_version":"1.0","event_id":"sha256:42f06aa41d6095f8eb3531667ccdf0262546a8cc1c06d06a40ffa02a2170a0bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GKUWJDQC6UTGJ5HUTAKVWSSKX6/bundle.json","state_url":"https://pith.science/pith/GKUWJDQC6UTGJ5HUTAKVWSSKX6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GKUWJDQC6UTGJ5HUTAKVWSSKX6/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":"2026-06-08T17:03:59Z","links":{"resolver":"https://pith.science/pith/GKUWJDQC6UTGJ5HUTAKVWSSKX6","bundle":"https://pith.science/pith/GKUWJDQC6UTGJ5HUTAKVWSSKX6/bundle.json","state":"https://pith.science/pith/GKUWJDQC6UTGJ5HUTAKVWSSKX6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GKUWJDQC6UTGJ5HUTAKVWSSKX6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GKUWJDQC6UTGJ5HUTAKVWSSKX6","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":"acb4cb7c7b83e5623ad67820088cdf10fdd875396b34f16e71a662a826a184e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-11-23T14:51:52Z","title_canon_sha256":"93c1fa99f42787bff6e1da122e5df049ce429fea0457d01dc8817eeac25eeeb6"},"schema_version":"1.0","source":{"id":"1511.07248","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.07248","created_at":"2026-05-18T01:20:29Z"},{"alias_kind":"arxiv_version","alias_value":"1511.07248v1","created_at":"2026-05-18T01:20:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07248","created_at":"2026-05-18T01:20:29Z"},{"alias_kind":"pith_short_12","alias_value":"GKUWJDQC6UTG","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GKUWJDQC6UTGJ5HU","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GKUWJDQC","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:42f06aa41d6095f8eb3531667ccdf0262546a8cc1c06d06a40ffa02a2170a0bb","target":"graph","created_at":"2026-05-18T01:20:29Z","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":"Complex networks have attracted growing attention in many fields. As a generalization of fractal analysis, multifractal analysis (MFA) is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. Some algorithms for MFA of unweighted complex networks have been proposed in the past a few years, including the sandbox (SB) algorithm recently employed by our group. In this paper, a modified SB algorithm (we call it SBw algorithm) is proposed for MFA of weighted networks.First, we use the SBw algorithm to study the multifractal property","authors_text":"Bao-Gen Li, Jin-Long Liu, Yu-Qin Song, Zu-Guo Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-11-23T14:51:52Z","title":"Multifractal analysis of weighted networks by a modified sandbox algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07248","kind":"arxiv","version":1},"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":"sha256:97f9e3a15a8707ab9ad17f141438cffdf3d4ba1dc64cc5606d4db870b72e606e","target":"record","created_at":"2026-05-18T01:20:29Z","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":"acb4cb7c7b83e5623ad67820088cdf10fdd875396b34f16e71a662a826a184e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-11-23T14:51:52Z","title_canon_sha256":"93c1fa99f42787bff6e1da122e5df049ce429fea0457d01dc8817eeac25eeeb6"},"schema_version":"1.0","source":{"id":"1511.07248","kind":"arxiv","version":1}},"canonical_sha256":"32a9648e02f52664f4f498155b4a4abfa339a10d0f15be557ee8058b08b8dacd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32a9648e02f52664f4f498155b4a4abfa339a10d0f15be557ee8058b08b8dacd","first_computed_at":"2026-05-18T01:20:29.082645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:29.082645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tQ0Da06FhPqx/RxmC/K9ToSZIHtEHxVXMZuGdMzbgstfixWI8SOaM1Iu5sld4tc9fsfIf+etTRnFBG7UW/1yBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:29.083249Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.07248","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97f9e3a15a8707ab9ad17f141438cffdf3d4ba1dc64cc5606d4db870b72e606e","sha256:42f06aa41d6095f8eb3531667ccdf0262546a8cc1c06d06a40ffa02a2170a0bb"],"state_sha256":"3b23fe62602505235c85a0f5dfc74c2f565f1f23d33d52822db8c345fd8bbd55"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DpbxvPLb0aKnSikX9sNQxSMF4oTolJZCJrYCHEouGqVRI4ZI2dRuoFA6Ja9OJC3gto0yzp2Q64Osqr/VByTgCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T17:03:59.614870Z","bundle_sha256":"79b77656ea5045afa831cf45f0ed22402cb1649961aad8cdbb255d8156c66cd4"}}