{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:FBE26NGXHYMFBKTBBYHXFE5PAT","short_pith_number":"pith:FBE26NGX","canonical_record":{"source":{"id":"1308.4621","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-08-21T16:08:52Z","cross_cats_sorted":[],"title_canon_sha256":"5e85783e7fcd611327964e112d74c1251159b7635f870ba18a084c057e73cf45","abstract_canon_sha256":"65df007b2b3b9fcc7f2c5985171d271a6d908a34762d60e48b41ee2e02726511"},"schema_version":"1.0"},"canonical_sha256":"2849af34d73e1850aa610e0f7293af04eedbcfa6063894640b7c8e30838508a4","source":{"kind":"arxiv","id":"1308.4621","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4621","created_at":"2026-05-18T03:15:21Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4621v1","created_at":"2026-05-18T03:15:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4621","created_at":"2026-05-18T03:15:21Z"},{"alias_kind":"pith_short_12","alias_value":"FBE26NGXHYMF","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FBE26NGXHYMFBKTB","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FBE26NGX","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:FBE26NGXHYMFBKTBBYHXFE5PAT","target":"record","payload":{"canonical_record":{"source":{"id":"1308.4621","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-08-21T16:08:52Z","cross_cats_sorted":[],"title_canon_sha256":"5e85783e7fcd611327964e112d74c1251159b7635f870ba18a084c057e73cf45","abstract_canon_sha256":"65df007b2b3b9fcc7f2c5985171d271a6d908a34762d60e48b41ee2e02726511"},"schema_version":"1.0"},"canonical_sha256":"2849af34d73e1850aa610e0f7293af04eedbcfa6063894640b7c8e30838508a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:21.499653Z","signature_b64":"LCYb3M2rHxKweaiZGnElKX/fWscSLel/a2Wb7lSC+wbU3o++QXMe1GZoa3PZnXdsoMeojM2/owZuL8s2HtsqBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2849af34d73e1850aa610e0f7293af04eedbcfa6063894640b7c8e30838508a4","last_reissued_at":"2026-05-18T03:15:21.498913Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:21.498913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.4621","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":"2026-05-18T03:15:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zIZq3p+RxUS2hGCUJBEC/7q7d0gIvgXoV2P/ey0BoDclkEZPbttVIt9ce7EsdIA3C/6PO0+R0jmZv9ibckcjBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:30:32.779994Z"},"content_sha256":"795f3d1e4180d6b6103a03c4409f5d4dca9e12463931294c7f8ba15c0d1f5fa7","schema_version":"1.0","event_id":"sha256:795f3d1e4180d6b6103a03c4409f5d4dca9e12463931294c7f8ba15c0d1f5fa7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:FBE26NGXHYMFBKTBBYHXFE5PAT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Understanding networks and their behaviors using sheaf theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Michael Robinson","submitted_at":"2013-08-21T16:08:52Z","abstract_excerpt":"Many complicated network problems can be easily understood on small networks. Difficulties arise when small networks are combined into larger ones. Fortunately, the mathematical theory of sheaves was constructed to address just this kind of situation; it extends locally-defined structures to globally valid inferences by way of consistency relations. This paper exhibits examples in network monitoring and filter hardware where sheaves have useful descriptive power."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4621","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":"2026-05-18T03:15:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1nMuWW36RDHVOPrjoO0dsBnxf2o7a9c3wuZPW8bOl8iBVPIeq/jQywQGxGn5s0UGL16PAdR+DwaS9MLruuRVCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:30:32.780344Z"},"content_sha256":"be43abbcb6f7e548df09f24d4df53301c0b058be2382ea43ce801f70ba92adbb","schema_version":"1.0","event_id":"sha256:be43abbcb6f7e548df09f24d4df53301c0b058be2382ea43ce801f70ba92adbb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FBE26NGXHYMFBKTBBYHXFE5PAT/bundle.json","state_url":"https://pith.science/pith/FBE26NGXHYMFBKTBBYHXFE5PAT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FBE26NGXHYMFBKTBBYHXFE5PAT/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":"2026-06-05T08:30:32Z","links":{"resolver":"https://pith.science/pith/FBE26NGXHYMFBKTBBYHXFE5PAT","bundle":"https://pith.science/pith/FBE26NGXHYMFBKTBBYHXFE5PAT/bundle.json","state":"https://pith.science/pith/FBE26NGXHYMFBKTBBYHXFE5PAT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FBE26NGXHYMFBKTBBYHXFE5PAT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FBE26NGXHYMFBKTBBYHXFE5PAT","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":"65df007b2b3b9fcc7f2c5985171d271a6d908a34762d60e48b41ee2e02726511","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-08-21T16:08:52Z","title_canon_sha256":"5e85783e7fcd611327964e112d74c1251159b7635f870ba18a084c057e73cf45"},"schema_version":"1.0","source":{"id":"1308.4621","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4621","created_at":"2026-05-18T03:15:21Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4621v1","created_at":"2026-05-18T03:15:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4621","created_at":"2026-05-18T03:15:21Z"},{"alias_kind":"pith_short_12","alias_value":"FBE26NGXHYMF","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FBE26NGXHYMFBKTB","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FBE26NGX","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:be43abbcb6f7e548df09f24d4df53301c0b058be2382ea43ce801f70ba92adbb","target":"graph","created_at":"2026-05-18T03:15:21Z","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":"Many complicated network problems can be easily understood on small networks. Difficulties arise when small networks are combined into larger ones. Fortunately, the mathematical theory of sheaves was constructed to address just this kind of situation; it extends locally-defined structures to globally valid inferences by way of consistency relations. This paper exhibits examples in network monitoring and filter hardware where sheaves have useful descriptive power.","authors_text":"Michael Robinson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-08-21T16:08:52Z","title":"Understanding networks and their behaviors using sheaf theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4621","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":"sha256:795f3d1e4180d6b6103a03c4409f5d4dca9e12463931294c7f8ba15c0d1f5fa7","target":"record","created_at":"2026-05-18T03:15:21Z","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":"65df007b2b3b9fcc7f2c5985171d271a6d908a34762d60e48b41ee2e02726511","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-08-21T16:08:52Z","title_canon_sha256":"5e85783e7fcd611327964e112d74c1251159b7635f870ba18a084c057e73cf45"},"schema_version":"1.0","source":{"id":"1308.4621","kind":"arxiv","version":1}},"canonical_sha256":"2849af34d73e1850aa610e0f7293af04eedbcfa6063894640b7c8e30838508a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2849af34d73e1850aa610e0f7293af04eedbcfa6063894640b7c8e30838508a4","first_computed_at":"2026-05-18T03:15:21.498913Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:21.498913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LCYb3M2rHxKweaiZGnElKX/fWscSLel/a2Wb7lSC+wbU3o++QXMe1GZoa3PZnXdsoMeojM2/owZuL8s2HtsqBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:21.499653Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4621","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:795f3d1e4180d6b6103a03c4409f5d4dca9e12463931294c7f8ba15c0d1f5fa7","sha256:be43abbcb6f7e548df09f24d4df53301c0b058be2382ea43ce801f70ba92adbb"],"state_sha256":"a0e0b195e5a8c86ed5401e777800e38a469f0e5c644acc165879a86f975273e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YBn62OZGcumio9wEjToe0zl54bvna1zTX348zYI1MCE/nZdHCkWpQmb/KLxOXgpA0184eTcbPVcAi6NK9oTLDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T08:30:32.782409Z","bundle_sha256":"fe90a18b3d17ac7ca8a288d55ebc31d06876289895eb676ed20132731447a90d"}}