{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:C7TZGDRAQ3DXQFLZZHUIGEXBDZ","short_pith_number":"pith:C7TZGDRA","canonical_record":{"source":{"id":"1411.7852","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-11-28T13:14:29Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"fc2b717442bcb3654d50608e9282c4c68bd3a1d8393607ac76134be105187f91","abstract_canon_sha256":"abf1682b881ad6408dd5329011ffeb082e0641395fee88e20acf909eb78188da"},"schema_version":"1.0"},"canonical_sha256":"17e7930e2086c7781579c9e88312e11e6481c78998ae04776d9170c7b8924721","source":{"kind":"arxiv","id":"1411.7852","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.7852","created_at":"2026-05-18T02:32:37Z"},{"alias_kind":"arxiv_version","alias_value":"1411.7852v1","created_at":"2026-05-18T02:32:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7852","created_at":"2026-05-18T02:32:37Z"},{"alias_kind":"pith_short_12","alias_value":"C7TZGDRAQ3DX","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"C7TZGDRAQ3DXQFLZ","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"C7TZGDRA","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:C7TZGDRAQ3DXQFLZZHUIGEXBDZ","target":"record","payload":{"canonical_record":{"source":{"id":"1411.7852","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-11-28T13:14:29Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"fc2b717442bcb3654d50608e9282c4c68bd3a1d8393607ac76134be105187f91","abstract_canon_sha256":"abf1682b881ad6408dd5329011ffeb082e0641395fee88e20acf909eb78188da"},"schema_version":"1.0"},"canonical_sha256":"17e7930e2086c7781579c9e88312e11e6481c78998ae04776d9170c7b8924721","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:37.115171Z","signature_b64":"fq2G6P7wPh8C5vCPGN1W1o3RdK8UmFMjIx/mq+tfECSgu2pTSFyxQvHfVmKV5zbxsGdcKkzqgZaw1JNwqcUjBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17e7930e2086c7781579c9e88312e11e6481c78998ae04776d9170c7b8924721","last_reissued_at":"2026-05-18T02:32:37.114072Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:37.114072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.7852","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":"2026-05-18T02:32:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dy+7pop2O/fpc7SFlR/B+/xU9LDh3U0rrCpQ85rt/eT2Kk/sN2s2ucjyOZZkviE6q1p5/KwyUP7WltWDOTJ1DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:42:04.494499Z"},"content_sha256":"02fa90fff55442d2b3bed316ae48ad9c297766f4eae2ab6364833f855f3f3f3a","schema_version":"1.0","event_id":"sha256:02fa90fff55442d2b3bed316ae48ad9c297766f4eae2ab6364833f855f3f3f3a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:C7TZGDRAQ3DXQFLZZHUIGEXBDZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterising actions on trees yielding non-trivial quasimorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Alessandra Iozzi, Alessandro Sisto, Cristina Pagliantini","submitted_at":"2014-11-28T13:14:29Z","abstract_excerpt":"We study the construction of quasimorphisms on groups acting on trees introduced by Monod and Shalom, that we call median quasimorphisms, and in particular we fully characterise actions on trees that give rise to non-trivial median quasimorphisms. Roughly speaking, either the action is highly transitive on geodesics, it fixes a point in the boundary, or there exists an infinite family of non-trivial median quasimorphisms. In particular, in the last case the second bounded cohomology of the group is infinite dimensional as a vector space. As an application, we show that a cocompact lattice in a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7852","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":"2026-05-18T02:32:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H7JxApWRLNhE8tYzFK5p781NAPOrKJue0s8yH+6sb3ApzBaB/WjT1Ja4XuINIT5T2LCN5gCe4q5CPKPfIOKZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:42:04.495124Z"},"content_sha256":"12d1793692f50935bedd2d41b1581a02f026ca6a956a5c7e117d65a159080fff","schema_version":"1.0","event_id":"sha256:12d1793692f50935bedd2d41b1581a02f026ca6a956a5c7e117d65a159080fff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C7TZGDRAQ3DXQFLZZHUIGEXBDZ/bundle.json","state_url":"https://pith.science/pith/C7TZGDRAQ3DXQFLZZHUIGEXBDZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C7TZGDRAQ3DXQFLZZHUIGEXBDZ/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":"2026-05-26T19:42:04Z","links":{"resolver":"https://pith.science/pith/C7TZGDRAQ3DXQFLZZHUIGEXBDZ","bundle":"https://pith.science/pith/C7TZGDRAQ3DXQFLZZHUIGEXBDZ/bundle.json","state":"https://pith.science/pith/C7TZGDRAQ3DXQFLZZHUIGEXBDZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C7TZGDRAQ3DXQFLZZHUIGEXBDZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:C7TZGDRAQ3DXQFLZZHUIGEXBDZ","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":"abf1682b881ad6408dd5329011ffeb082e0641395fee88e20acf909eb78188da","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-11-28T13:14:29Z","title_canon_sha256":"fc2b717442bcb3654d50608e9282c4c68bd3a1d8393607ac76134be105187f91"},"schema_version":"1.0","source":{"id":"1411.7852","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.7852","created_at":"2026-05-18T02:32:37Z"},{"alias_kind":"arxiv_version","alias_value":"1411.7852v1","created_at":"2026-05-18T02:32:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7852","created_at":"2026-05-18T02:32:37Z"},{"alias_kind":"pith_short_12","alias_value":"C7TZGDRAQ3DX","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"C7TZGDRAQ3DXQFLZ","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"C7TZGDRA","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:12d1793692f50935bedd2d41b1581a02f026ca6a956a5c7e117d65a159080fff","target":"graph","created_at":"2026-05-18T02:32:37Z","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 construction of quasimorphisms on groups acting on trees introduced by Monod and Shalom, that we call median quasimorphisms, and in particular we fully characterise actions on trees that give rise to non-trivial median quasimorphisms. Roughly speaking, either the action is highly transitive on geodesics, it fixes a point in the boundary, or there exists an infinite family of non-trivial median quasimorphisms. In particular, in the last case the second bounded cohomology of the group is infinite dimensional as a vector space. As an application, we show that a cocompact lattice in a","authors_text":"Alessandra Iozzi, Alessandro Sisto, Cristina Pagliantini","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-11-28T13:14:29Z","title":"Characterising actions on trees yielding non-trivial quasimorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7852","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":"sha256:02fa90fff55442d2b3bed316ae48ad9c297766f4eae2ab6364833f855f3f3f3a","target":"record","created_at":"2026-05-18T02:32:37Z","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":"abf1682b881ad6408dd5329011ffeb082e0641395fee88e20acf909eb78188da","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-11-28T13:14:29Z","title_canon_sha256":"fc2b717442bcb3654d50608e9282c4c68bd3a1d8393607ac76134be105187f91"},"schema_version":"1.0","source":{"id":"1411.7852","kind":"arxiv","version":1}},"canonical_sha256":"17e7930e2086c7781579c9e88312e11e6481c78998ae04776d9170c7b8924721","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17e7930e2086c7781579c9e88312e11e6481c78998ae04776d9170c7b8924721","first_computed_at":"2026-05-18T02:32:37.114072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:37.114072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fq2G6P7wPh8C5vCPGN1W1o3RdK8UmFMjIx/mq+tfECSgu2pTSFyxQvHfVmKV5zbxsGdcKkzqgZaw1JNwqcUjBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:37.115171Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.7852","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02fa90fff55442d2b3bed316ae48ad9c297766f4eae2ab6364833f855f3f3f3a","sha256:12d1793692f50935bedd2d41b1581a02f026ca6a956a5c7e117d65a159080fff"],"state_sha256":"8fd5e485d61179b6859d003c2ac685eabe1ae317a5641f0696563947ef5e9b74"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lBcZuQTQmYTVlHwdODCYxPZC3D4itOb4BDNd1Dmk/WjiScY9ycYReb69Ht6X1p/H4OF2QSBK7YYbq1IFI+eIBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T19:42:04.498706Z","bundle_sha256":"8d36b8f56f6a32c328ee44323db98e7b512448f7de486bad0a4104b0516fa054"}}