{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GEDL2VFAMD3ZIZZZPFIDXVPO2Q","short_pith_number":"pith:GEDL2VFA","canonical_record":{"source":{"id":"1103.4893","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2011-03-25T01:42:03Z","cross_cats_sorted":["math.CA","math.DS","math.OC","nlin.AO"],"title_canon_sha256":"dc7bd4ffe22a29ee30e63ef9dc5354d50b729b01474fc03c7e9404123f1ba19e","abstract_canon_sha256":"91a87783e3673df781b48988943051bd8c72379d5e7292ceac3ab7787a02445c"},"schema_version":"1.0"},"canonical_sha256":"3106bd54a060f794673979503bd5eed427e59d7cb627485a89bb3a230c949de2","source":{"kind":"arxiv","id":"1103.4893","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4893","created_at":"2026-05-18T04:25:48Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4893v1","created_at":"2026-05-18T04:25:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4893","created_at":"2026-05-18T04:25:48Z"},{"alias_kind":"pith_short_12","alias_value":"GEDL2VFAMD3Z","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GEDL2VFAMD3ZIZZZ","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GEDL2VFA","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GEDL2VFAMD3ZIZZZPFIDXVPO2Q","target":"record","payload":{"canonical_record":{"source":{"id":"1103.4893","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2011-03-25T01:42:03Z","cross_cats_sorted":["math.CA","math.DS","math.OC","nlin.AO"],"title_canon_sha256":"dc7bd4ffe22a29ee30e63ef9dc5354d50b729b01474fc03c7e9404123f1ba19e","abstract_canon_sha256":"91a87783e3673df781b48988943051bd8c72379d5e7292ceac3ab7787a02445c"},"schema_version":"1.0"},"canonical_sha256":"3106bd54a060f794673979503bd5eed427e59d7cb627485a89bb3a230c949de2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:48.456263Z","signature_b64":"jZMn24GtG95tBkwHeMVdvA603b7ZUHAh8xXlZDhlms6DgGNkwxn3n2CplOYNVbXLtADIoAWYNJRWDfn5AN9QCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3106bd54a060f794673979503bd5eed427e59d7cb627485a89bb3a230c949de2","last_reissued_at":"2026-05-18T04:25:48.455735Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:48.455735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.4893","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":"2026-05-18T04:25:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zN+RcjxV2KSWxVVjz2sD3/clUZr6Sl71e+6mBm9BZKBbStWnpjcckxBghbGHenos7hYGOjHwFws0GkE/ArkuCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T10:14:00.066770Z"},"content_sha256":"3cf51a8fc03594fd558cc7f7d012e648a6dcca9046667d38ee68f1ff7b180fdf","schema_version":"1.0","event_id":"sha256:3cf51a8fc03594fd558cc7f7d012e648a6dcca9046667d38ee68f1ff7b180fdf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GEDL2VFAMD3ZIZZZPFIDXVPO2Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Robust Distributed Routing in Dynamical Flow Networks - Part II: Strong Resilience, Equilibrium Selection and Cascaded Failures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.DS","math.OC","nlin.AO"],"primary_cat":"cs.SY","authors_text":"Daron Acemoglu, Emilio Frazzoli, Giacomo Como, Ketan Savla, Munther A. Dahleh","submitted_at":"2011-03-25T01:42:03Z","abstract_excerpt":"Strong resilience properties of dynamical flow networks are analyzed for distributed routing policies. The latter are characterized by the property that the way the inflow at a non-destination node gets split among its outgoing links is allowed to depend only on local information about the current particle densities on the outgoing links. The strong resilience of the network is defined as the infimum sum of link-wise flow capacity reductions under which the network cannot maintain the asymptotic total inflow to the destination node to be equal to the inflow at the origin. A class of distribute"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4893","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":"2026-05-18T04:25:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qqX/OaJjHp2BYPPvmO6CwVhsLl7PF3nVoegOrZRqT9ZQCoTEBZFIVaBPmuKXltAn55iTwyaNqQQlP3v4sbqJAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T10:14:00.067139Z"},"content_sha256":"412de0ebb91a7ffdd501523e51885771048f606adb1f208c4f6df0c6d8c311e7","schema_version":"1.0","event_id":"sha256:412de0ebb91a7ffdd501523e51885771048f606adb1f208c4f6df0c6d8c311e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GEDL2VFAMD3ZIZZZPFIDXVPO2Q/bundle.json","state_url":"https://pith.science/pith/GEDL2VFAMD3ZIZZZPFIDXVPO2Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GEDL2VFAMD3ZIZZZPFIDXVPO2Q/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":"2026-06-28T10:14:00Z","links":{"resolver":"https://pith.science/pith/GEDL2VFAMD3ZIZZZPFIDXVPO2Q","bundle":"https://pith.science/pith/GEDL2VFAMD3ZIZZZPFIDXVPO2Q/bundle.json","state":"https://pith.science/pith/GEDL2VFAMD3ZIZZZPFIDXVPO2Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GEDL2VFAMD3ZIZZZPFIDXVPO2Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GEDL2VFAMD3ZIZZZPFIDXVPO2Q","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":"91a87783e3673df781b48988943051bd8c72379d5e7292ceac3ab7787a02445c","cross_cats_sorted":["math.CA","math.DS","math.OC","nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2011-03-25T01:42:03Z","title_canon_sha256":"dc7bd4ffe22a29ee30e63ef9dc5354d50b729b01474fc03c7e9404123f1ba19e"},"schema_version":"1.0","source":{"id":"1103.4893","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4893","created_at":"2026-05-18T04:25:48Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4893v1","created_at":"2026-05-18T04:25:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4893","created_at":"2026-05-18T04:25:48Z"},{"alias_kind":"pith_short_12","alias_value":"GEDL2VFAMD3Z","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GEDL2VFAMD3ZIZZZ","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GEDL2VFA","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:412de0ebb91a7ffdd501523e51885771048f606adb1f208c4f6df0c6d8c311e7","target":"graph","created_at":"2026-05-18T04:25:48Z","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":"Strong resilience properties of dynamical flow networks are analyzed for distributed routing policies. The latter are characterized by the property that the way the inflow at a non-destination node gets split among its outgoing links is allowed to depend only on local information about the current particle densities on the outgoing links. The strong resilience of the network is defined as the infimum sum of link-wise flow capacity reductions under which the network cannot maintain the asymptotic total inflow to the destination node to be equal to the inflow at the origin. A class of distribute","authors_text":"Daron Acemoglu, Emilio Frazzoli, Giacomo Como, Ketan Savla, Munther A. Dahleh","cross_cats":["math.CA","math.DS","math.OC","nlin.AO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2011-03-25T01:42:03Z","title":"Robust Distributed Routing in Dynamical Flow Networks - Part II: Strong Resilience, Equilibrium Selection and Cascaded Failures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4893","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":"sha256:3cf51a8fc03594fd558cc7f7d012e648a6dcca9046667d38ee68f1ff7b180fdf","target":"record","created_at":"2026-05-18T04:25:48Z","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":"91a87783e3673df781b48988943051bd8c72379d5e7292ceac3ab7787a02445c","cross_cats_sorted":["math.CA","math.DS","math.OC","nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2011-03-25T01:42:03Z","title_canon_sha256":"dc7bd4ffe22a29ee30e63ef9dc5354d50b729b01474fc03c7e9404123f1ba19e"},"schema_version":"1.0","source":{"id":"1103.4893","kind":"arxiv","version":1}},"canonical_sha256":"3106bd54a060f794673979503bd5eed427e59d7cb627485a89bb3a230c949de2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3106bd54a060f794673979503bd5eed427e59d7cb627485a89bb3a230c949de2","first_computed_at":"2026-05-18T04:25:48.455735Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:48.455735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jZMn24GtG95tBkwHeMVdvA603b7ZUHAh8xXlZDhlms6DgGNkwxn3n2CplOYNVbXLtADIoAWYNJRWDfn5AN9QCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:48.456263Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.4893","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3cf51a8fc03594fd558cc7f7d012e648a6dcca9046667d38ee68f1ff7b180fdf","sha256:412de0ebb91a7ffdd501523e51885771048f606adb1f208c4f6df0c6d8c311e7"],"state_sha256":"572ad3dc5a6f277e37f1825b139b06214192328b0f798582d377a945eaf447d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lMmSQ91azC5sMuBDbPIaQI6EZtUpr3JQPxOhHZaFgHJhHX77jBdGcc9/BeanUpMdhB16ZXQHa0QJFPMLVAbFBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T10:14:00.069039Z","bundle_sha256":"b581b44c2af4ef4ae29d829e97e8a0c06139bf5ffd987270598aea4d5ac6ab45"}}