{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3VPIKNJIBJMWFD5DDF4RSFCC3F","short_pith_number":"pith:3VPIKNJI","canonical_record":{"source":{"id":"1705.07995","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2017-05-22T20:48:56Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"37b3c9fb44e4704faf18ec16f7deff31b9079f9a1afc59f681fee873f86abae9","abstract_canon_sha256":"784518bb9903e9dc0981a43441ff2eecb93230164d597036fc272dc58dc0f8b5"},"schema_version":"1.0"},"canonical_sha256":"dd5e8535280a59628fa31979191442d942affbf910c62487e2a35a9105746288","source":{"kind":"arxiv","id":"1705.07995","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.07995","created_at":"2026-05-18T00:29:40Z"},{"alias_kind":"arxiv_version","alias_value":"1705.07995v2","created_at":"2026-05-18T00:29:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07995","created_at":"2026-05-18T00:29:40Z"},{"alias_kind":"pith_short_12","alias_value":"3VPIKNJIBJMW","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3VPIKNJIBJMWFD5D","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3VPIKNJI","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3VPIKNJIBJMWFD5DDF4RSFCC3F","target":"record","payload":{"canonical_record":{"source":{"id":"1705.07995","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2017-05-22T20:48:56Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"37b3c9fb44e4704faf18ec16f7deff31b9079f9a1afc59f681fee873f86abae9","abstract_canon_sha256":"784518bb9903e9dc0981a43441ff2eecb93230164d597036fc272dc58dc0f8b5"},"schema_version":"1.0"},"canonical_sha256":"dd5e8535280a59628fa31979191442d942affbf910c62487e2a35a9105746288","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:40.876539Z","signature_b64":"cPU4Qt2Q6k1NtC2GMAmyZUZ3Je9BRgX4bHv7t8ZxfrGK68zpflX+14URCYtFsG+E1h/pUCLzfWBkqM2I6J4fBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd5e8535280a59628fa31979191442d942affbf910c62487e2a35a9105746288","last_reissued_at":"2026-05-18T00:29:40.875993Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:40.875993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.07995","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"csVZIyp0EpP/QIukfT/+/oMnlkeTNdd0Ee6IYK8qD4dZ0yionJEQ8QcE+oY82pbpK470bC9HYQVl0NPW0COwCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T08:55:27.073098Z"},"content_sha256":"ffcac44b886d24e73624b1486c1db3ec2e64edef7ff7cf0bd0ad07334cd28328","schema_version":"1.0","event_id":"sha256:ffcac44b886d24e73624b1486c1db3ec2e64edef7ff7cf0bd0ad07334cd28328"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3VPIKNJIBJMWFD5DDF4RSFCC3F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Theorem of the heart in negative K-theory for weight structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.KT","authors_text":"Vladimir Sosnilo","submitted_at":"2017-05-22T20:48:56Z","abstract_excerpt":"We construct the strong weight complex functor (in the sense of Bondarko) for a stable infinity-category $\\underline{C}$ equipped with a bounded weight structure $w$. Along the way we prove that $\\underline{C}$ is determined by the infinity-categorical heart of $w$. This allows us to compare the K-theory of $\\underline{C}$ and the K-theory of $\\underline{Hw}$, the classical heart of $w$. In particular, we prove that $\\operatorname{K}_{n}(\\underline{C}) \\to \\operatorname{K}_{n}(\\underline{Hw})$ are isomorphisms for $n \\le 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07995","kind":"arxiv","version":2},"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":"2026-05-18T00:29:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bX3BR6OBSzbz5kL84Rf4kst4Sxvr3kfib9p000bsWiyRZShQIniMLy14HgjoxF4PMi878NOXn64RVYHmHBV5BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T08:55:27.073738Z"},"content_sha256":"0b9abd7e026691aa170cfd05865cfc07ee03b0b1f00e7642c62d116f2506bb5a","schema_version":"1.0","event_id":"sha256:0b9abd7e026691aa170cfd05865cfc07ee03b0b1f00e7642c62d116f2506bb5a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3VPIKNJIBJMWFD5DDF4RSFCC3F/bundle.json","state_url":"https://pith.science/pith/3VPIKNJIBJMWFD5DDF4RSFCC3F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3VPIKNJIBJMWFD5DDF4RSFCC3F/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":"2026-06-21T08:55:27Z","links":{"resolver":"https://pith.science/pith/3VPIKNJIBJMWFD5DDF4RSFCC3F","bundle":"https://pith.science/pith/3VPIKNJIBJMWFD5DDF4RSFCC3F/bundle.json","state":"https://pith.science/pith/3VPIKNJIBJMWFD5DDF4RSFCC3F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3VPIKNJIBJMWFD5DDF4RSFCC3F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3VPIKNJIBJMWFD5DDF4RSFCC3F","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":"784518bb9903e9dc0981a43441ff2eecb93230164d597036fc272dc58dc0f8b5","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2017-05-22T20:48:56Z","title_canon_sha256":"37b3c9fb44e4704faf18ec16f7deff31b9079f9a1afc59f681fee873f86abae9"},"schema_version":"1.0","source":{"id":"1705.07995","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.07995","created_at":"2026-05-18T00:29:40Z"},{"alias_kind":"arxiv_version","alias_value":"1705.07995v2","created_at":"2026-05-18T00:29:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07995","created_at":"2026-05-18T00:29:40Z"},{"alias_kind":"pith_short_12","alias_value":"3VPIKNJIBJMW","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3VPIKNJIBJMWFD5D","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3VPIKNJI","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:0b9abd7e026691aa170cfd05865cfc07ee03b0b1f00e7642c62d116f2506bb5a","target":"graph","created_at":"2026-05-18T00:29:40Z","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 construct the strong weight complex functor (in the sense of Bondarko) for a stable infinity-category $\\underline{C}$ equipped with a bounded weight structure $w$. Along the way we prove that $\\underline{C}$ is determined by the infinity-categorical heart of $w$. This allows us to compare the K-theory of $\\underline{C}$ and the K-theory of $\\underline{Hw}$, the classical heart of $w$. In particular, we prove that $\\operatorname{K}_{n}(\\underline{C}) \\to \\operatorname{K}_{n}(\\underline{Hw})$ are isomorphisms for $n \\le 0$.","authors_text":"Vladimir Sosnilo","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2017-05-22T20:48:56Z","title":"Theorem of the heart in negative K-theory for weight structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07995","kind":"arxiv","version":2},"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:ffcac44b886d24e73624b1486c1db3ec2e64edef7ff7cf0bd0ad07334cd28328","target":"record","created_at":"2026-05-18T00:29:40Z","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":"784518bb9903e9dc0981a43441ff2eecb93230164d597036fc272dc58dc0f8b5","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2017-05-22T20:48:56Z","title_canon_sha256":"37b3c9fb44e4704faf18ec16f7deff31b9079f9a1afc59f681fee873f86abae9"},"schema_version":"1.0","source":{"id":"1705.07995","kind":"arxiv","version":2}},"canonical_sha256":"dd5e8535280a59628fa31979191442d942affbf910c62487e2a35a9105746288","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd5e8535280a59628fa31979191442d942affbf910c62487e2a35a9105746288","first_computed_at":"2026-05-18T00:29:40.875993Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:40.875993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cPU4Qt2Q6k1NtC2GMAmyZUZ3Je9BRgX4bHv7t8ZxfrGK68zpflX+14URCYtFsG+E1h/pUCLzfWBkqM2I6J4fBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:40.876539Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.07995","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffcac44b886d24e73624b1486c1db3ec2e64edef7ff7cf0bd0ad07334cd28328","sha256:0b9abd7e026691aa170cfd05865cfc07ee03b0b1f00e7642c62d116f2506bb5a"],"state_sha256":"ff230c16a77715f4cbb23d93bd8a0b13c4e3a33fdddb03cb7c1f298d4111a2cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1qOr1HeRhtxaWlAYRlpIIxre+8oG5cJBw+/7TjDZGKBo2JPt1ifSN47GHmObExjPnZhCTY/FtTpIXwvV/R1rAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T08:55:27.077333Z","bundle_sha256":"8d2ae7de2bb19a36df6ba6db04acc373ffbfc2bf54a99d33f48634bdf9c18810"}}