{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:QX2DFSICCXQBVP7XWEODDYVLVJ","short_pith_number":"pith:QX2DFSIC","canonical_record":{"source":{"id":"2403.06030","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2024-03-09T22:34:24Z","cross_cats_sorted":["math.DS","math.KT"],"title_canon_sha256":"6a34374e7f64354ca768c586f58a9bdc6aaa6c9f22e3c4e60362a51f93255e6a","abstract_canon_sha256":"d2c90756d2c51a4dab8e44b26fb59c1ef540a484d9f66f151aef767a3a897a9a"},"schema_version":"1.0"},"canonical_sha256":"85f432c90215e01abff7b11c31e2abaa7b4836cf0e9616b47d9c12da99cbd7de","source":{"kind":"arxiv","id":"2403.06030","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.06030","created_at":"2026-07-05T07:54:17Z"},{"alias_kind":"arxiv_version","alias_value":"2403.06030v1","created_at":"2026-07-05T07:54:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.06030","created_at":"2026-07-05T07:54:17Z"},{"alias_kind":"pith_short_12","alias_value":"QX2DFSICCXQB","created_at":"2026-07-05T07:54:17Z"},{"alias_kind":"pith_short_16","alias_value":"QX2DFSICCXQBVP7X","created_at":"2026-07-05T07:54:17Z"},{"alias_kind":"pith_short_8","alias_value":"QX2DFSIC","created_at":"2026-07-05T07:54:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:QX2DFSICCXQBVP7XWEODDYVLVJ","target":"record","payload":{"canonical_record":{"source":{"id":"2403.06030","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2024-03-09T22:34:24Z","cross_cats_sorted":["math.DS","math.KT"],"title_canon_sha256":"6a34374e7f64354ca768c586f58a9bdc6aaa6c9f22e3c4e60362a51f93255e6a","abstract_canon_sha256":"d2c90756d2c51a4dab8e44b26fb59c1ef540a484d9f66f151aef767a3a897a9a"},"schema_version":"1.0"},"canonical_sha256":"85f432c90215e01abff7b11c31e2abaa7b4836cf0e9616b47d9c12da99cbd7de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:54:17.048688Z","signature_b64":"9PYmQomvxE/+x3xPj7jen94SN5M+trFd5jbt04J2sx0FJrdNNuLSPWk7zFJB+umRDsXitArNO0ym2v3iCLnzAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85f432c90215e01abff7b11c31e2abaa7b4836cf0e9616b47d9c12da99cbd7de","last_reissued_at":"2026-07-05T07:54:17.048324Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:54:17.048324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.06030","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":"2026-07-05T07:54:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3n+mVyubNvwH+uqAeOv1Invk+bGP6qjPra5It84lEkz8rkyBy5pxfQgA8QE00IzZ2u+YadEjl2Jup07wcw1GBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T12:39:12.014251Z"},"content_sha256":"e9d0d9f59c913be0f3794a89c8a64a09363ad10680bf034012a3fb5fb2386e57","schema_version":"1.0","event_id":"sha256:e9d0d9f59c913be0f3794a89c8a64a09363ad10680bf034012a3fb5fb2386e57"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:QX2DFSICCXQBVP7XWEODDYVLVJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Foam cobordism and the Sah-Arnoux-Fathi invariant","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS","math.KT"],"primary_cat":"math.GT","authors_text":"Mee Seong Im, Mikhail Khovanov","submitted_at":"2024-03-09T22:34:24Z","abstract_excerpt":"This is the first in a series of papers where scissor congruence and K-theoretical invariants are related to cobordism groups of foams in various dimensions. A model example is provided where the cobordism group of weighted one-foams is identified, via the Sah-Arnoux-Fathi invariant, with the first homology of the group of interval exchange automorphisms and with the Zakharevich first K-group of the corresponding assembler. Several variations on this cobordism group are computed as well."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.06030","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.06030/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:54:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QVy9jFzNAOXYe5/UJKUz/Rqr7BnQ4oXPZ5GE6GKBHnO+TRAEsadMlbdSJptu0gZ5oDipx3V2LuXKJ/33F4UNDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T12:39:12.014758Z"},"content_sha256":"d672fc57679c98aaff6a74369a103439b0780d63099c9fa09c95715e9288285f","schema_version":"1.0","event_id":"sha256:d672fc57679c98aaff6a74369a103439b0780d63099c9fa09c95715e9288285f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QX2DFSICCXQBVP7XWEODDYVLVJ/bundle.json","state_url":"https://pith.science/pith/QX2DFSICCXQBVP7XWEODDYVLVJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QX2DFSICCXQBVP7XWEODDYVLVJ/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":"2026-08-12T12:39:12Z","links":{"resolver":"https://pith.science/pith/QX2DFSICCXQBVP7XWEODDYVLVJ","bundle":"https://pith.science/pith/QX2DFSICCXQBVP7XWEODDYVLVJ/bundle.json","state":"https://pith.science/pith/QX2DFSICCXQBVP7XWEODDYVLVJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QX2DFSICCXQBVP7XWEODDYVLVJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QX2DFSICCXQBVP7XWEODDYVLVJ","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":"d2c90756d2c51a4dab8e44b26fb59c1ef540a484d9f66f151aef767a3a897a9a","cross_cats_sorted":["math.DS","math.KT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2024-03-09T22:34:24Z","title_canon_sha256":"6a34374e7f64354ca768c586f58a9bdc6aaa6c9f22e3c4e60362a51f93255e6a"},"schema_version":"1.0","source":{"id":"2403.06030","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.06030","created_at":"2026-07-05T07:54:17Z"},{"alias_kind":"arxiv_version","alias_value":"2403.06030v1","created_at":"2026-07-05T07:54:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.06030","created_at":"2026-07-05T07:54:17Z"},{"alias_kind":"pith_short_12","alias_value":"QX2DFSICCXQB","created_at":"2026-07-05T07:54:17Z"},{"alias_kind":"pith_short_16","alias_value":"QX2DFSICCXQBVP7X","created_at":"2026-07-05T07:54:17Z"},{"alias_kind":"pith_short_8","alias_value":"QX2DFSIC","created_at":"2026-07-05T07:54:17Z"}],"graph_snapshots":[{"event_id":"sha256:d672fc57679c98aaff6a74369a103439b0780d63099c9fa09c95715e9288285f","target":"graph","created_at":"2026-07-05T07:54:17Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2403.06030/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This is the first in a series of papers where scissor congruence and K-theoretical invariants are related to cobordism groups of foams in various dimensions. A model example is provided where the cobordism group of weighted one-foams is identified, via the Sah-Arnoux-Fathi invariant, with the first homology of the group of interval exchange automorphisms and with the Zakharevich first K-group of the corresponding assembler. Several variations on this cobordism group are computed as well.","authors_text":"Mee Seong Im, Mikhail Khovanov","cross_cats":["math.DS","math.KT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2024-03-09T22:34:24Z","title":"Foam cobordism and the Sah-Arnoux-Fathi invariant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.06030","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:e9d0d9f59c913be0f3794a89c8a64a09363ad10680bf034012a3fb5fb2386e57","target":"record","created_at":"2026-07-05T07:54:17Z","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":"d2c90756d2c51a4dab8e44b26fb59c1ef540a484d9f66f151aef767a3a897a9a","cross_cats_sorted":["math.DS","math.KT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2024-03-09T22:34:24Z","title_canon_sha256":"6a34374e7f64354ca768c586f58a9bdc6aaa6c9f22e3c4e60362a51f93255e6a"},"schema_version":"1.0","source":{"id":"2403.06030","kind":"arxiv","version":1}},"canonical_sha256":"85f432c90215e01abff7b11c31e2abaa7b4836cf0e9616b47d9c12da99cbd7de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85f432c90215e01abff7b11c31e2abaa7b4836cf0e9616b47d9c12da99cbd7de","first_computed_at":"2026-07-05T07:54:17.048324Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:54:17.048324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9PYmQomvxE/+x3xPj7jen94SN5M+trFd5jbt04J2sx0FJrdNNuLSPWk7zFJB+umRDsXitArNO0ym2v3iCLnzAg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:54:17.048688Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.06030","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9d0d9f59c913be0f3794a89c8a64a09363ad10680bf034012a3fb5fb2386e57","sha256:d672fc57679c98aaff6a74369a103439b0780d63099c9fa09c95715e9288285f"],"state_sha256":"280323e8a3e57405cb4479b0ffbad3dbc178237036a5f105283d131f630615bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7auAndtZdYism9QAeA/Hqi9neCHickk1JqSVcZDoMTKVJEA1knCeunDpHz8hKCHPDPBGkEzJfIfxlhCFk2shCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T12:39:12.019397Z","bundle_sha256":"a0942fca098ecdde53f97228fe8a5b469326752b9b1687a2a98cacf6d57483ad"}}