{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:M64SOG4K5V3Z4K7TWCMBQUSUKR","short_pith_number":"pith:M64SOG4K","canonical_record":{"source":{"id":"2007.14938","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-07-29T16:24:37Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"85c6946a3c96b6aa3162d8ca98d6a4875de763d618cd465ab40088e4f784b7e7","abstract_canon_sha256":"8c78961711fe00deb517f0be446a6ab8e418cd4158f2ff1b9ad39f6142492e01"},"schema_version":"1.0"},"canonical_sha256":"67b9271b8aed779e2bf3b098185254545472c8e65e10ab1ee981eac184bd516f","source":{"kind":"arxiv","id":"2007.14938","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.14938","created_at":"2026-07-05T01:26:42Z"},{"alias_kind":"arxiv_version","alias_value":"2007.14938v1","created_at":"2026-07-05T01:26:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.14938","created_at":"2026-07-05T01:26:42Z"},{"alias_kind":"pith_short_12","alias_value":"M64SOG4K5V3Z","created_at":"2026-07-05T01:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"M64SOG4K5V3Z4K7T","created_at":"2026-07-05T01:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"M64SOG4K","created_at":"2026-07-05T01:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:M64SOG4K5V3Z4K7TWCMBQUSUKR","target":"record","payload":{"canonical_record":{"source":{"id":"2007.14938","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-07-29T16:24:37Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"85c6946a3c96b6aa3162d8ca98d6a4875de763d618cd465ab40088e4f784b7e7","abstract_canon_sha256":"8c78961711fe00deb517f0be446a6ab8e418cd4158f2ff1b9ad39f6142492e01"},"schema_version":"1.0"},"canonical_sha256":"67b9271b8aed779e2bf3b098185254545472c8e65e10ab1ee981eac184bd516f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:26:42.222794Z","signature_b64":"QAo9QOztiIXNV0k7xvjNCGJ8tg50r92WsO5rkIKkAogHe4NkyZ4w4VryxdcgHZ9vCdcFnjRdyKlXWADyfGk9CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67b9271b8aed779e2bf3b098185254545472c8e65e10ab1ee981eac184bd516f","last_reissued_at":"2026-07-05T01:26:42.222358Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:26:42.222358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2007.14938","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":"2026-07-05T01:26:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lNY8HVDtY4qTvd1MdLUntP5MkJeqphyPLgb9ERfjuWWn16VDOBigbkjSDUloAf8qA0c5SrjHwA+IqI311IBLAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T14:28:22.112853Z"},"content_sha256":"453d8a2b21424c610a2c03d412edf366a37deba1ae9da6dc0e6ff6b656ce939b","schema_version":"1.0","event_id":"sha256:453d8a2b21424c610a2c03d412edf366a37deba1ae9da6dc0e6ff6b656ce939b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:M64SOG4K5V3Z4K7TWCMBQUSUKR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cache-enabled HetNets with Limited Backhaul: A Stochastic Geometry Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Congshan Fan, Tiankui Zhang, Yuanwei Liu, Zhiming Zeng","submitted_at":"2020-07-29T16:24:37Z","abstract_excerpt":"With the rapid explosion of data volume from mobile networks, edge caching has received significant attentions as an efficient approach to boost content delivery efficiency by bringing contents near users. In this article, cache-enabled heterogeneous networks (HetNets) considering the limited backhaul is analyzed with the aid of the stochastic geometry approach. A hybrid caching policy, in which the most popular contents are cached in the macro BSs tier with the deterministic caching strategy and the less popular contents are cached in the helpers tier with the probabilistic caching strategy, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.14938","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2007.14938/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:26:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bq67hx93qhhHEcVu6VJ8StH6WQDwA+HurgEqLaQKXa32DpmE3nqKh0l0TJ4SpFXf2ZrimtAOKqYjqPw4VwILDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T14:28:22.113502Z"},"content_sha256":"f04aac75ad13dd1a18b5c2a53f4938fc02958dbc4973472f29971891a8c404f2","schema_version":"1.0","event_id":"sha256:f04aac75ad13dd1a18b5c2a53f4938fc02958dbc4973472f29971891a8c404f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M64SOG4K5V3Z4K7TWCMBQUSUKR/bundle.json","state_url":"https://pith.science/pith/M64SOG4K5V3Z4K7TWCMBQUSUKR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M64SOG4K5V3Z4K7TWCMBQUSUKR/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":"2026-08-23T14:28:22Z","links":{"resolver":"https://pith.science/pith/M64SOG4K5V3Z4K7TWCMBQUSUKR","bundle":"https://pith.science/pith/M64SOG4K5V3Z4K7TWCMBQUSUKR/bundle.json","state":"https://pith.science/pith/M64SOG4K5V3Z4K7TWCMBQUSUKR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M64SOG4K5V3Z4K7TWCMBQUSUKR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:M64SOG4K5V3Z4K7TWCMBQUSUKR","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":"8c78961711fe00deb517f0be446a6ab8e418cd4158f2ff1b9ad39f6142492e01","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-07-29T16:24:37Z","title_canon_sha256":"85c6946a3c96b6aa3162d8ca98d6a4875de763d618cd465ab40088e4f784b7e7"},"schema_version":"1.0","source":{"id":"2007.14938","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.14938","created_at":"2026-07-05T01:26:42Z"},{"alias_kind":"arxiv_version","alias_value":"2007.14938v1","created_at":"2026-07-05T01:26:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.14938","created_at":"2026-07-05T01:26:42Z"},{"alias_kind":"pith_short_12","alias_value":"M64SOG4K5V3Z","created_at":"2026-07-05T01:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"M64SOG4K5V3Z4K7T","created_at":"2026-07-05T01:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"M64SOG4K","created_at":"2026-07-05T01:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:f04aac75ad13dd1a18b5c2a53f4938fc02958dbc4973472f29971891a8c404f2","target":"graph","created_at":"2026-07-05T01:26:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2007.14938/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"With the rapid explosion of data volume from mobile networks, edge caching has received significant attentions as an efficient approach to boost content delivery efficiency by bringing contents near users. In this article, cache-enabled heterogeneous networks (HetNets) considering the limited backhaul is analyzed with the aid of the stochastic geometry approach. A hybrid caching policy, in which the most popular contents are cached in the macro BSs tier with the deterministic caching strategy and the less popular contents are cached in the helpers tier with the probabilistic caching strategy, ","authors_text":"Congshan Fan, Tiankui Zhang, Yuanwei Liu, Zhiming Zeng","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-07-29T16:24:37Z","title":"Cache-enabled HetNets with Limited Backhaul: A Stochastic Geometry Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.14938","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":"sha256:453d8a2b21424c610a2c03d412edf366a37deba1ae9da6dc0e6ff6b656ce939b","target":"record","created_at":"2026-07-05T01:26:42Z","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":"8c78961711fe00deb517f0be446a6ab8e418cd4158f2ff1b9ad39f6142492e01","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-07-29T16:24:37Z","title_canon_sha256":"85c6946a3c96b6aa3162d8ca98d6a4875de763d618cd465ab40088e4f784b7e7"},"schema_version":"1.0","source":{"id":"2007.14938","kind":"arxiv","version":1}},"canonical_sha256":"67b9271b8aed779e2bf3b098185254545472c8e65e10ab1ee981eac184bd516f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67b9271b8aed779e2bf3b098185254545472c8e65e10ab1ee981eac184bd516f","first_computed_at":"2026-07-05T01:26:42.222358Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:26:42.222358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QAo9QOztiIXNV0k7xvjNCGJ8tg50r92WsO5rkIKkAogHe4NkyZ4w4VryxdcgHZ9vCdcFnjRdyKlXWADyfGk9CA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:26:42.222794Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.14938","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:453d8a2b21424c610a2c03d412edf366a37deba1ae9da6dc0e6ff6b656ce939b","sha256:f04aac75ad13dd1a18b5c2a53f4938fc02958dbc4973472f29971891a8c404f2"],"state_sha256":"4740ed353069a21106857db5a35a2af20d85460305ddb4d1c2b6fe9a931346b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ery0iTMJ0Yoms53Jzxb0r2gYSk2Yk9zpfTOPhh3a8RDvHiW3AH8Ho/G6A9OTCiCdBrTi3y/sjOVp6poqyJEwAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T14:28:22.118980Z","bundle_sha256":"d6d746c792b1f217894cd46697093d99536f553e6f10788dfc86ca079c767d2e"}}