{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:VS7HOS6IUUEHF4WJBBIWQJMGQ4","short_pith_number":"pith:VS7HOS6I","canonical_record":{"source":{"id":"1106.5387","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-06-27T13:19:08Z","cross_cats_sorted":["cs.NI","math.IT"],"title_canon_sha256":"acda5643eaf315b700a191cb96ed436c606732d9f0a1944e51ae8d1d5241beb3","abstract_canon_sha256":"efa639a4d66de36f82612bcfc8d139e8fa8e7c4c7a70da134509d63a2c88506f"},"schema_version":"1.0"},"canonical_sha256":"acbe774bc8a50872f2c908516825868714db1faf2ed8c8b6a7ca1c7b4da65e87","source":{"kind":"arxiv","id":"1106.5387","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5387","created_at":"2026-05-18T00:58:18Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5387v2","created_at":"2026-05-18T00:58:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5387","created_at":"2026-05-18T00:58:18Z"},{"alias_kind":"pith_short_12","alias_value":"VS7HOS6IUUEH","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VS7HOS6IUUEHF4WJ","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VS7HOS6I","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:VS7HOS6IUUEHF4WJBBIWQJMGQ4","target":"record","payload":{"canonical_record":{"source":{"id":"1106.5387","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-06-27T13:19:08Z","cross_cats_sorted":["cs.NI","math.IT"],"title_canon_sha256":"acda5643eaf315b700a191cb96ed436c606732d9f0a1944e51ae8d1d5241beb3","abstract_canon_sha256":"efa639a4d66de36f82612bcfc8d139e8fa8e7c4c7a70da134509d63a2c88506f"},"schema_version":"1.0"},"canonical_sha256":"acbe774bc8a50872f2c908516825868714db1faf2ed8c8b6a7ca1c7b4da65e87","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:18.881421Z","signature_b64":"BtbuVEPAcGtEXz3pxR2CLDci6usj1O/fI83oXTKy35ZdlXttcBykX0hh4gHau/k/71kCm6JSondlxl8RTFgSDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"acbe774bc8a50872f2c908516825868714db1faf2ed8c8b6a7ca1c7b4da65e87","last_reissued_at":"2026-05-18T00:58:18.880728Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:18.880728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.5387","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":"2026-05-18T00:58:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dXJXPLZjqJ2KotutZgiC4J/R3EhIjeuRIfxccGXmoAgVEWKVmbJ5ydkBEd+NVren5eAANE8m8G8xhS3mZ4DaBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:05:06.436480Z"},"content_sha256":"2600ebe8f6b573aeb7f415079d521dd022833a3b871cd75817c17ffcc449ec78","schema_version":"1.0","event_id":"sha256:2600ebe8f6b573aeb7f415079d521dd022833a3b871cd75817c17ffcc449ec78"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:VS7HOS6IUUEHF4WJBBIWQJMGQ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subspace Properties of Network Coding and their Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NI","math.IT"],"primary_cat":"cs.IT","authors_text":"Christina Fragouli, Mahdi Jafari Siavoshani, Suhas Diggavi","submitted_at":"2011-06-27T13:19:08Z","abstract_excerpt":"Systems that employ network coding for content distribution convey to the receivers linear combinations of the source packets. If we assume randomized network coding, during this process the network nodes collect random subspaces of the space spanned by the source packets. We establish several fundamental properties of the random subspaces induced in such a system, and show that these subspaces implicitly carry topological information about the network and its state that can be passively collected and inferred. We leverage this information towards a number of applications that are interesting "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5387","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":"2026-05-18T00:58:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/77nIrRAF6s8CZFCiCuh/sBekYpIbkELVKylor0s8hdp3bcBOu0qdvUCoH1zePo27hQL8IGrJJjCG5CvBs73Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:05:06.436887Z"},"content_sha256":"65c100eed8362c4592cefc1e01ba1e89c3bf990026c411bf11e6e85941284f45","schema_version":"1.0","event_id":"sha256:65c100eed8362c4592cefc1e01ba1e89c3bf990026c411bf11e6e85941284f45"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VS7HOS6IUUEHF4WJBBIWQJMGQ4/bundle.json","state_url":"https://pith.science/pith/VS7HOS6IUUEHF4WJBBIWQJMGQ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VS7HOS6IUUEHF4WJBBIWQJMGQ4/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":"2026-05-30T20:05:06Z","links":{"resolver":"https://pith.science/pith/VS7HOS6IUUEHF4WJBBIWQJMGQ4","bundle":"https://pith.science/pith/VS7HOS6IUUEHF4WJBBIWQJMGQ4/bundle.json","state":"https://pith.science/pith/VS7HOS6IUUEHF4WJBBIWQJMGQ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VS7HOS6IUUEHF4WJBBIWQJMGQ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VS7HOS6IUUEHF4WJBBIWQJMGQ4","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":"efa639a4d66de36f82612bcfc8d139e8fa8e7c4c7a70da134509d63a2c88506f","cross_cats_sorted":["cs.NI","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-06-27T13:19:08Z","title_canon_sha256":"acda5643eaf315b700a191cb96ed436c606732d9f0a1944e51ae8d1d5241beb3"},"schema_version":"1.0","source":{"id":"1106.5387","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5387","created_at":"2026-05-18T00:58:18Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5387v2","created_at":"2026-05-18T00:58:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5387","created_at":"2026-05-18T00:58:18Z"},{"alias_kind":"pith_short_12","alias_value":"VS7HOS6IUUEH","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VS7HOS6IUUEHF4WJ","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VS7HOS6I","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:65c100eed8362c4592cefc1e01ba1e89c3bf990026c411bf11e6e85941284f45","target":"graph","created_at":"2026-05-18T00:58:18Z","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":"Systems that employ network coding for content distribution convey to the receivers linear combinations of the source packets. If we assume randomized network coding, during this process the network nodes collect random subspaces of the space spanned by the source packets. We establish several fundamental properties of the random subspaces induced in such a system, and show that these subspaces implicitly carry topological information about the network and its state that can be passively collected and inferred. We leverage this information towards a number of applications that are interesting ","authors_text":"Christina Fragouli, Mahdi Jafari Siavoshani, Suhas Diggavi","cross_cats":["cs.NI","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-06-27T13:19:08Z","title":"Subspace Properties of Network Coding and their Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5387","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":"sha256:2600ebe8f6b573aeb7f415079d521dd022833a3b871cd75817c17ffcc449ec78","target":"record","created_at":"2026-05-18T00:58:18Z","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":"efa639a4d66de36f82612bcfc8d139e8fa8e7c4c7a70da134509d63a2c88506f","cross_cats_sorted":["cs.NI","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-06-27T13:19:08Z","title_canon_sha256":"acda5643eaf315b700a191cb96ed436c606732d9f0a1944e51ae8d1d5241beb3"},"schema_version":"1.0","source":{"id":"1106.5387","kind":"arxiv","version":2}},"canonical_sha256":"acbe774bc8a50872f2c908516825868714db1faf2ed8c8b6a7ca1c7b4da65e87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"acbe774bc8a50872f2c908516825868714db1faf2ed8c8b6a7ca1c7b4da65e87","first_computed_at":"2026-05-18T00:58:18.880728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:18.880728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BtbuVEPAcGtEXz3pxR2CLDci6usj1O/fI83oXTKy35ZdlXttcBykX0hh4gHau/k/71kCm6JSondlxl8RTFgSDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:18.881421Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.5387","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2600ebe8f6b573aeb7f415079d521dd022833a3b871cd75817c17ffcc449ec78","sha256:65c100eed8362c4592cefc1e01ba1e89c3bf990026c411bf11e6e85941284f45"],"state_sha256":"00ebcb67dd52e3a39c71df75d9f2c5b5b021f41820b7b2a032b0a10c61cc72db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LMpJ8PRDZ4zrQKN9FLK7YnPn766bQpPD1JMO4Hp37DoaHiJCSn2wiO2etmRPg+rpTbF3RJY5bjZRXwy6PRcgBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T20:05:06.440829Z","bundle_sha256":"c44a9f5553c9323e3fcdc2323ac7d5101204aee3bffe012b72801d91d1c8a498"}}