{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:O6WTRWFUX5Q2G5OD3NRRZLQAYA","short_pith_number":"pith:O6WTRWFU","canonical_record":{"source":{"id":"1405.5979","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-23T07:45:17Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"9b8aa632a0bdbe3059d687a0027325aeb8b707ce0a95469ac7797b1d290563d7","abstract_canon_sha256":"0f3e53e3475d4d7876f3282bb487d4a297a8d728c61edb2e8ecaf7a2c835075e"},"schema_version":"1.0"},"canonical_sha256":"77ad38d8b4bf61a375c3db631cae00c02b0a353cd7065d70b454d8f7eb8d5301","source":{"kind":"arxiv","id":"1405.5979","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.5979","created_at":"2026-05-18T00:33:33Z"},{"alias_kind":"arxiv_version","alias_value":"1405.5979v4","created_at":"2026-05-18T00:33:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5979","created_at":"2026-05-18T00:33:33Z"},{"alias_kind":"pith_short_12","alias_value":"O6WTRWFUX5Q2","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O6WTRWFUX5Q2G5OD","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O6WTRWFU","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:O6WTRWFUX5Q2G5OD3NRRZLQAYA","target":"record","payload":{"canonical_record":{"source":{"id":"1405.5979","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-23T07:45:17Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"9b8aa632a0bdbe3059d687a0027325aeb8b707ce0a95469ac7797b1d290563d7","abstract_canon_sha256":"0f3e53e3475d4d7876f3282bb487d4a297a8d728c61edb2e8ecaf7a2c835075e"},"schema_version":"1.0"},"canonical_sha256":"77ad38d8b4bf61a375c3db631cae00c02b0a353cd7065d70b454d8f7eb8d5301","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:33.010040Z","signature_b64":"gRCKF4vYnTrYg3c40j9b8a6dgzcmQSmwZux9kVvMGYpqjAdARj86HyTbClkqAPOngu1H6t83HDE9iNge04YBAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77ad38d8b4bf61a375c3db631cae00c02b0a353cd7065d70b454d8f7eb8d5301","last_reissued_at":"2026-05-18T00:33:33.009482Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:33.009482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.5979","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gjOFyRwW1yQmRSFYl9TpFr1+/mgTzg1nV7GOhFCTiVqrK+GDwmteKNQPagSMCtPm3Ns6vds+lMLncvftA/wpAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:13:42.841150Z"},"content_sha256":"12869a823adc3032ce8c58e0700d8d060a64da72d391eb6380debf3b4142c6f9","schema_version":"1.0","event_id":"sha256:12869a823adc3032ce8c58e0700d8d060a64da72d391eb6380debf3b4142c6f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:O6WTRWFUX5Q2G5OD3NRRZLQAYA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lossy gossip and composition of metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Andries E. Brouwer, Bart J. Frenk, Jan Draisma","submitted_at":"2014-05-23T07:45:17Z","abstract_excerpt":"We study the monoid generated by n-by-n distance matrices under tropical (or min-plus) multiplication. Using the tropical geometry of the orthogonal group, we prove that this monoid is a finite polyhedral fan of dimension n(n-1)/2, and we compute the structure of this fan for n up to 5. The monoid captures gossip among n gossipers over lossy phone lines, and contains the gossip monoid over ordinary phone lines as a submonoid. We prove several new results about this submonoid, as well. In particular, we establish a sharp bound on chains of calls in each of which someone learns something new."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5979","kind":"arxiv","version":4},"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":"2026-05-18T00:33:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AX9/o8jx41RdLscsPmBvjcZOjw8VE5RKA3kGUDZTwU3X2vJWg3155EPFTcrBjDZlkdgspn/j1ZIDEfk4fsisBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:13:42.841495Z"},"content_sha256":"62d88930cf21344b6e5bce9ad2c1f28def167e8346b7df6d073201acf20ecdfe","schema_version":"1.0","event_id":"sha256:62d88930cf21344b6e5bce9ad2c1f28def167e8346b7df6d073201acf20ecdfe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O6WTRWFUX5Q2G5OD3NRRZLQAYA/bundle.json","state_url":"https://pith.science/pith/O6WTRWFUX5Q2G5OD3NRRZLQAYA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O6WTRWFUX5Q2G5OD3NRRZLQAYA/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":"2026-06-01T19:13:42Z","links":{"resolver":"https://pith.science/pith/O6WTRWFUX5Q2G5OD3NRRZLQAYA","bundle":"https://pith.science/pith/O6WTRWFUX5Q2G5OD3NRRZLQAYA/bundle.json","state":"https://pith.science/pith/O6WTRWFUX5Q2G5OD3NRRZLQAYA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O6WTRWFUX5Q2G5OD3NRRZLQAYA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:O6WTRWFUX5Q2G5OD3NRRZLQAYA","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":"0f3e53e3475d4d7876f3282bb487d4a297a8d728c61edb2e8ecaf7a2c835075e","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-23T07:45:17Z","title_canon_sha256":"9b8aa632a0bdbe3059d687a0027325aeb8b707ce0a95469ac7797b1d290563d7"},"schema_version":"1.0","source":{"id":"1405.5979","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.5979","created_at":"2026-05-18T00:33:33Z"},{"alias_kind":"arxiv_version","alias_value":"1405.5979v4","created_at":"2026-05-18T00:33:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5979","created_at":"2026-05-18T00:33:33Z"},{"alias_kind":"pith_short_12","alias_value":"O6WTRWFUX5Q2","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O6WTRWFUX5Q2G5OD","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O6WTRWFU","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:62d88930cf21344b6e5bce9ad2c1f28def167e8346b7df6d073201acf20ecdfe","target":"graph","created_at":"2026-05-18T00:33:33Z","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":"We study the monoid generated by n-by-n distance matrices under tropical (or min-plus) multiplication. Using the tropical geometry of the orthogonal group, we prove that this monoid is a finite polyhedral fan of dimension n(n-1)/2, and we compute the structure of this fan for n up to 5. The monoid captures gossip among n gossipers over lossy phone lines, and contains the gossip monoid over ordinary phone lines as a submonoid. We prove several new results about this submonoid, as well. In particular, we establish a sharp bound on chains of calls in each of which someone learns something new.","authors_text":"Andries E. Brouwer, Bart J. Frenk, Jan Draisma","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-23T07:45:17Z","title":"Lossy gossip and composition of metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5979","kind":"arxiv","version":4},"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":"sha256:12869a823adc3032ce8c58e0700d8d060a64da72d391eb6380debf3b4142c6f9","target":"record","created_at":"2026-05-18T00:33:33Z","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":"0f3e53e3475d4d7876f3282bb487d4a297a8d728c61edb2e8ecaf7a2c835075e","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-23T07:45:17Z","title_canon_sha256":"9b8aa632a0bdbe3059d687a0027325aeb8b707ce0a95469ac7797b1d290563d7"},"schema_version":"1.0","source":{"id":"1405.5979","kind":"arxiv","version":4}},"canonical_sha256":"77ad38d8b4bf61a375c3db631cae00c02b0a353cd7065d70b454d8f7eb8d5301","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77ad38d8b4bf61a375c3db631cae00c02b0a353cd7065d70b454d8f7eb8d5301","first_computed_at":"2026-05-18T00:33:33.009482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:33.009482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gRCKF4vYnTrYg3c40j9b8a6dgzcmQSmwZux9kVvMGYpqjAdARj86HyTbClkqAPOngu1H6t83HDE9iNge04YBAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:33.010040Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.5979","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12869a823adc3032ce8c58e0700d8d060a64da72d391eb6380debf3b4142c6f9","sha256:62d88930cf21344b6e5bce9ad2c1f28def167e8346b7df6d073201acf20ecdfe"],"state_sha256":"0e0d1996509f20cedebb77342d9e6cde605e7fbd879a7f8ff6da1928effba0c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I3hilIw/DzM2kAwV6lc3YYhY9jiutnosdihPC/C/1KWE7wvs4yp42HnQnHd4YOK3PGcqP56dwpXicsWNlr+oDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:13:42.843297Z","bundle_sha256":"13c90cc550d18d0639986b2b577ae5c97c7448284918b37122280421ce84c96c"}}