{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:V7SBBW7GDVCOUYCXZN3N6NMWB2","short_pith_number":"pith:V7SBBW7G","canonical_record":{"source":{"id":"1705.09751","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.IT","submitted_at":"2017-05-27T01:33:30Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d825a2e52a18d3bb5ff467230a1be173678dbecbe7c24c76427d789e8c9a13b3","abstract_canon_sha256":"b3a43c5ebdd1d76d2606018d029e5e4fd3fdacf6698409bfde287863817b2780"},"schema_version":"1.0"},"canonical_sha256":"afe410dbe61d44ea6057cb76df35960ea1f802c05c92feeb46214b7f29dc91fd","source":{"kind":"arxiv","id":"1705.09751","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.09751","created_at":"2026-05-18T00:43:34Z"},{"alias_kind":"arxiv_version","alias_value":"1705.09751v1","created_at":"2026-05-18T00:43:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09751","created_at":"2026-05-18T00:43:34Z"},{"alias_kind":"pith_short_12","alias_value":"V7SBBW7GDVCO","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V7SBBW7GDVCOUYCX","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V7SBBW7G","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:V7SBBW7GDVCOUYCXZN3N6NMWB2","target":"record","payload":{"canonical_record":{"source":{"id":"1705.09751","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.IT","submitted_at":"2017-05-27T01:33:30Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d825a2e52a18d3bb5ff467230a1be173678dbecbe7c24c76427d789e8c9a13b3","abstract_canon_sha256":"b3a43c5ebdd1d76d2606018d029e5e4fd3fdacf6698409bfde287863817b2780"},"schema_version":"1.0"},"canonical_sha256":"afe410dbe61d44ea6057cb76df35960ea1f802c05c92feeb46214b7f29dc91fd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:34.568838Z","signature_b64":"NB9JdS7wufoWV6beEDm0YYLMN/BiuJpYuQ/4IvxKdgWxO9jI5x5j8UQYxQU8FErutYX3QC7YzODW/77JpXaqCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afe410dbe61d44ea6057cb76df35960ea1f802c05c92feeb46214b7f29dc91fd","last_reissued_at":"2026-05-18T00:43:34.568291Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:34.568291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.09751","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":"2026-05-18T00:43:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FOC1F/TYrQ9XdLQDJjEFS3BZ1qMC2mck2W3RdrSHCwFotKwDBDXPaLvCEcSVMxZyrxV8ce/+jFMMVBXHhekuDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:54:33.628364Z"},"content_sha256":"c798c83bdd6a8d05ee7b417a098511662470763c0bc88fcc699410ac1fdf13eb","schema_version":"1.0","event_id":"sha256:c798c83bdd6a8d05ee7b417a098511662470763c0bc88fcc699410ac1fdf13eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:V7SBBW7GDVCOUYCXZN3N6NMWB2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Capacity of Fractal Wireless Networks With Direct Social Interactions","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Honggang Zhang, Rongpeng Li, Ying Chen, Zhifeng Zhao","submitted_at":"2017-05-27T01:33:30Z","abstract_excerpt":"The capacity of a fractal wireless network with direct social interactions is studied in this paper. Specifically, we mathematically formulate the self-similarity of a fractal wireless network by a power-law degree distribution $ P(k) $, and we capture the connection feature between two nodes with degree $ k_{1} $ and $ k_{2} $ by a joint probability distribution $ P(k_{1},k_{2}) $. It is proved that if the source node communicates with one of its direct contacts randomly, the maximum capacity is consistent with the classical result $ \\Theta\\left(\\frac{1}{\\sqrt{n\\log n}}\\right) $ achieved by K"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09751","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":"2026-05-18T00:43:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TYkFELvkxG1oIiFJolSm5N4GjYuS6by54IRHtvrBe5DiBjHPQwhBP/HxPJBCIxBnvorFj6Hx50XUMvNuE8N+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:54:33.629103Z"},"content_sha256":"dfb8f2286ce1e2a591e243b45511793ed594bfc8816c9ec78c36bed24c9ba82d","schema_version":"1.0","event_id":"sha256:dfb8f2286ce1e2a591e243b45511793ed594bfc8816c9ec78c36bed24c9ba82d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V7SBBW7GDVCOUYCXZN3N6NMWB2/bundle.json","state_url":"https://pith.science/pith/V7SBBW7GDVCOUYCXZN3N6NMWB2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V7SBBW7GDVCOUYCXZN3N6NMWB2/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":"2026-06-04T22:54:33Z","links":{"resolver":"https://pith.science/pith/V7SBBW7GDVCOUYCXZN3N6NMWB2","bundle":"https://pith.science/pith/V7SBBW7GDVCOUYCXZN3N6NMWB2/bundle.json","state":"https://pith.science/pith/V7SBBW7GDVCOUYCXZN3N6NMWB2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V7SBBW7GDVCOUYCXZN3N6NMWB2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:V7SBBW7GDVCOUYCXZN3N6NMWB2","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":"b3a43c5ebdd1d76d2606018d029e5e4fd3fdacf6698409bfde287863817b2780","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.IT","submitted_at":"2017-05-27T01:33:30Z","title_canon_sha256":"d825a2e52a18d3bb5ff467230a1be173678dbecbe7c24c76427d789e8c9a13b3"},"schema_version":"1.0","source":{"id":"1705.09751","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.09751","created_at":"2026-05-18T00:43:34Z"},{"alias_kind":"arxiv_version","alias_value":"1705.09751v1","created_at":"2026-05-18T00:43:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09751","created_at":"2026-05-18T00:43:34Z"},{"alias_kind":"pith_short_12","alias_value":"V7SBBW7GDVCO","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V7SBBW7GDVCOUYCX","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V7SBBW7G","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:dfb8f2286ce1e2a591e243b45511793ed594bfc8816c9ec78c36bed24c9ba82d","target":"graph","created_at":"2026-05-18T00:43:34Z","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":"The capacity of a fractal wireless network with direct social interactions is studied in this paper. Specifically, we mathematically formulate the self-similarity of a fractal wireless network by a power-law degree distribution $ P(k) $, and we capture the connection feature between two nodes with degree $ k_{1} $ and $ k_{2} $ by a joint probability distribution $ P(k_{1},k_{2}) $. It is proved that if the source node communicates with one of its direct contacts randomly, the maximum capacity is consistent with the classical result $ \\Theta\\left(\\frac{1}{\\sqrt{n\\log n}}\\right) $ achieved by K","authors_text":"Honggang Zhang, Rongpeng Li, Ying Chen, Zhifeng Zhao","cross_cats":["math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.IT","submitted_at":"2017-05-27T01:33:30Z","title":"On the Capacity of Fractal Wireless Networks With Direct Social Interactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09751","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:c798c83bdd6a8d05ee7b417a098511662470763c0bc88fcc699410ac1fdf13eb","target":"record","created_at":"2026-05-18T00:43:34Z","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":"b3a43c5ebdd1d76d2606018d029e5e4fd3fdacf6698409bfde287863817b2780","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.IT","submitted_at":"2017-05-27T01:33:30Z","title_canon_sha256":"d825a2e52a18d3bb5ff467230a1be173678dbecbe7c24c76427d789e8c9a13b3"},"schema_version":"1.0","source":{"id":"1705.09751","kind":"arxiv","version":1}},"canonical_sha256":"afe410dbe61d44ea6057cb76df35960ea1f802c05c92feeb46214b7f29dc91fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afe410dbe61d44ea6057cb76df35960ea1f802c05c92feeb46214b7f29dc91fd","first_computed_at":"2026-05-18T00:43:34.568291Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:34.568291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NB9JdS7wufoWV6beEDm0YYLMN/BiuJpYuQ/4IvxKdgWxO9jI5x5j8UQYxQU8FErutYX3QC7YzODW/77JpXaqCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:34.568838Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.09751","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c798c83bdd6a8d05ee7b417a098511662470763c0bc88fcc699410ac1fdf13eb","sha256:dfb8f2286ce1e2a591e243b45511793ed594bfc8816c9ec78c36bed24c9ba82d"],"state_sha256":"a6f7ef41ccb657f1541908c9e01f13e859ba60e47786173b1b3dc0eccece6d85"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rmlgtOBAPSK55i1xz1kUA9lp6egoTkiudIGXlBtTrB8lul8h9Eoh6qbrX3zAtxwuCkglYuiayYg+ddXucUo1CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T22:54:33.632303Z","bundle_sha256":"e76c7bfb54b3a574b696ab14572fd03c73bf88de0d8a37340f093be0c256f542"}}