{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7RPW3N6KQ6UYQZ5FHFBHSDGVCT","short_pith_number":"pith:7RPW3N6K","canonical_record":{"source":{"id":"1605.04093","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-05-13T09:15:09Z","cross_cats_sorted":[],"title_canon_sha256":"c73b8304f533d5023229ef1638a1d79a6a469ea3d1c300673c9882fb00008f75","abstract_canon_sha256":"7c6e68694775a62d8255606a7a0ac7caf7dd4ec2fd121cd1e43fd302c53a673f"},"schema_version":"1.0"},"canonical_sha256":"fc5f6db7ca87a98867a53942790cd514f00ee6f0b407e3dc364576d9efb1d3d5","source":{"kind":"arxiv","id":"1605.04093","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.04093","created_at":"2026-05-17T23:50:16Z"},{"alias_kind":"arxiv_version","alias_value":"1605.04093v1","created_at":"2026-05-17T23:50:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.04093","created_at":"2026-05-17T23:50:16Z"},{"alias_kind":"pith_short_12","alias_value":"7RPW3N6KQ6UY","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7RPW3N6KQ6UYQZ5F","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7RPW3N6K","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7RPW3N6KQ6UYQZ5FHFBHSDGVCT","target":"record","payload":{"canonical_record":{"source":{"id":"1605.04093","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-05-13T09:15:09Z","cross_cats_sorted":[],"title_canon_sha256":"c73b8304f533d5023229ef1638a1d79a6a469ea3d1c300673c9882fb00008f75","abstract_canon_sha256":"7c6e68694775a62d8255606a7a0ac7caf7dd4ec2fd121cd1e43fd302c53a673f"},"schema_version":"1.0"},"canonical_sha256":"fc5f6db7ca87a98867a53942790cd514f00ee6f0b407e3dc364576d9efb1d3d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:16.646561Z","signature_b64":"8Q3mxqsX49HXi1+a2szN9GX8ezcMa6qSQDPfNpYmdE56APuYoqecd46GcUVARzfRO7tUtehB8OF5R9eeet5+DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc5f6db7ca87a98867a53942790cd514f00ee6f0b407e3dc364576d9efb1d3d5","last_reissued_at":"2026-05-17T23:50:16.645976Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:16.645976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.04093","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":"2026-05-17T23:50:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bieA8Njyw1PmB7xdPE4XTy0oG7t+KzNvjs3oQjB8nwwnttR7d1nU39xoQ1APwmHfitZw6QG4aIZMMy0SSA+KBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:31:22.636246Z"},"content_sha256":"a8af8e2259e531a487e24197c030a18b17f32bc0f7da00c8ce98a3c1bb4e473d","schema_version":"1.0","event_id":"sha256:a8af8e2259e531a487e24197c030a18b17f32bc0f7da00c8ce98a3c1bb4e473d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7RPW3N6KQ6UYQZ5FHFBHSDGVCT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exotic finite functorial semi-norms on singular homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Clara Loeh, Daniel Fauser","submitted_at":"2016-05-13T09:15:09Z","abstract_excerpt":"Functorial semi-norms on singular homology give refined \"size\" information on singular homology classes. A fundamental example is the l^1-semi-norm. We show that there exist finite functorial semi-norms on singular homology that are exotic in the sense that they are not carried by the l^1-semi-norm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04093","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":"2026-05-17T23:50:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vouCe7zzHF3SucOawdZXiQ8HbLReGbLoDLvbWZSMr+3MiCJb9QuqNsUMAnnhB9M0EOMw529q3/NQpBgbcwTmCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:31:22.636947Z"},"content_sha256":"bfbfa1f7c65cb5b227fb05d645e7d3b38c1796f04daaa8f61e225133ed498807","schema_version":"1.0","event_id":"sha256:bfbfa1f7c65cb5b227fb05d645e7d3b38c1796f04daaa8f61e225133ed498807"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7RPW3N6KQ6UYQZ5FHFBHSDGVCT/bundle.json","state_url":"https://pith.science/pith/7RPW3N6KQ6UYQZ5FHFBHSDGVCT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7RPW3N6KQ6UYQZ5FHFBHSDGVCT/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":"2026-06-06T14:31:22Z","links":{"resolver":"https://pith.science/pith/7RPW3N6KQ6UYQZ5FHFBHSDGVCT","bundle":"https://pith.science/pith/7RPW3N6KQ6UYQZ5FHFBHSDGVCT/bundle.json","state":"https://pith.science/pith/7RPW3N6KQ6UYQZ5FHFBHSDGVCT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7RPW3N6KQ6UYQZ5FHFBHSDGVCT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7RPW3N6KQ6UYQZ5FHFBHSDGVCT","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":"7c6e68694775a62d8255606a7a0ac7caf7dd4ec2fd121cd1e43fd302c53a673f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-05-13T09:15:09Z","title_canon_sha256":"c73b8304f533d5023229ef1638a1d79a6a469ea3d1c300673c9882fb00008f75"},"schema_version":"1.0","source":{"id":"1605.04093","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.04093","created_at":"2026-05-17T23:50:16Z"},{"alias_kind":"arxiv_version","alias_value":"1605.04093v1","created_at":"2026-05-17T23:50:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.04093","created_at":"2026-05-17T23:50:16Z"},{"alias_kind":"pith_short_12","alias_value":"7RPW3N6KQ6UY","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7RPW3N6KQ6UYQZ5F","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7RPW3N6K","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:bfbfa1f7c65cb5b227fb05d645e7d3b38c1796f04daaa8f61e225133ed498807","target":"graph","created_at":"2026-05-17T23:50:16Z","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":"Functorial semi-norms on singular homology give refined \"size\" information on singular homology classes. A fundamental example is the l^1-semi-norm. We show that there exist finite functorial semi-norms on singular homology that are exotic in the sense that they are not carried by the l^1-semi-norm.","authors_text":"Clara Loeh, Daniel Fauser","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-05-13T09:15:09Z","title":"Exotic finite functorial semi-norms on singular homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04093","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:a8af8e2259e531a487e24197c030a18b17f32bc0f7da00c8ce98a3c1bb4e473d","target":"record","created_at":"2026-05-17T23:50:16Z","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":"7c6e68694775a62d8255606a7a0ac7caf7dd4ec2fd121cd1e43fd302c53a673f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-05-13T09:15:09Z","title_canon_sha256":"c73b8304f533d5023229ef1638a1d79a6a469ea3d1c300673c9882fb00008f75"},"schema_version":"1.0","source":{"id":"1605.04093","kind":"arxiv","version":1}},"canonical_sha256":"fc5f6db7ca87a98867a53942790cd514f00ee6f0b407e3dc364576d9efb1d3d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc5f6db7ca87a98867a53942790cd514f00ee6f0b407e3dc364576d9efb1d3d5","first_computed_at":"2026-05-17T23:50:16.645976Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:16.645976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8Q3mxqsX49HXi1+a2szN9GX8ezcMa6qSQDPfNpYmdE56APuYoqecd46GcUVARzfRO7tUtehB8OF5R9eeet5+DQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:16.646561Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.04093","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8af8e2259e531a487e24197c030a18b17f32bc0f7da00c8ce98a3c1bb4e473d","sha256:bfbfa1f7c65cb5b227fb05d645e7d3b38c1796f04daaa8f61e225133ed498807"],"state_sha256":"e5378e7475431059d97997bf8f773da11014c9b5ec99f4163e2a2e5bfcf1e462"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wOauCKkjmicLZ/l7O30RIBcg46H2sEqCTPGCrZ6PiWIH31b5iB1RkL9X6rnn3vaY/aOZPKoYdL+uXfqZD1l0Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T14:31:22.640756Z","bundle_sha256":"831925562cf58a49610e3eae87b5f08cee7a2c73569a6a21a24b7d037832ec5e"}}