{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:232SD5UD6JLMZH6HWONA7CLT35","short_pith_number":"pith:232SD5UD","canonical_record":{"source":{"id":"1706.00042","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-31T18:24:20Z","cross_cats_sorted":[],"title_canon_sha256":"23864f053094c355c54adc46326386ffde99f3bb8c0f5daa501055b76f23fe65","abstract_canon_sha256":"ce274f37c008fb0ef1695f933d119a45af73d52bf6ec036188b2fa2b91df0aa3"},"schema_version":"1.0"},"canonical_sha256":"d6f521f683f256cc9fc7b39a0f8973df63e5927f1d92ac3d3123a586b33e30a7","source":{"kind":"arxiv","id":"1706.00042","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00042","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00042v2","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00042","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"232SD5UD6JLM","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"232SD5UD6JLMZH6H","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"232SD5UD","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:232SD5UD6JLMZH6HWONA7CLT35","target":"record","payload":{"canonical_record":{"source":{"id":"1706.00042","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-31T18:24:20Z","cross_cats_sorted":[],"title_canon_sha256":"23864f053094c355c54adc46326386ffde99f3bb8c0f5daa501055b76f23fe65","abstract_canon_sha256":"ce274f37c008fb0ef1695f933d119a45af73d52bf6ec036188b2fa2b91df0aa3"},"schema_version":"1.0"},"canonical_sha256":"d6f521f683f256cc9fc7b39a0f8973df63e5927f1d92ac3d3123a586b33e30a7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:23.316103Z","signature_b64":"FpSPR8zw4z09u8gFCwyhmovIzwwOmi1O+WE8L8U6Sd4/lBKvJSNUo7ustDcfhsiajrJKT4GI71zKiPfdtjvuDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6f521f683f256cc9fc7b39a0f8973df63e5927f1d92ac3d3123a586b33e30a7","last_reissued_at":"2026-05-18T00:42:23.315601Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:23.315601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.00042","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":"2026-05-18T00:42:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xyPoRvc70nJwhh6g4CWZUBEiLe3RbpO9QIYa8ejCsFQl3H+OqEg0UlJopvXSw1lpmhsAFFiJ7i+xtUn4VkAxAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T10:09:38.772173Z"},"content_sha256":"f44bd5decfd1e609048d190b327fd0ec973843f084f8d6bc550ff1b3c5918feb","schema_version":"1.0","event_id":"sha256:f44bd5decfd1e609048d190b327fd0ec973843f084f8d6bc550ff1b3c5918feb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:232SD5UD6JLMZH6HWONA7CLT35","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A problem on partial sums in abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anita Pasotti, Fiorenza Morini, Marco Antonio Pellegrini, Simone Costa","submitted_at":"2017-05-31T18:24:20Z","abstract_excerpt":"In this paper we propose a conjecture concerning partial sums of an arbitrary finite subset of an abelian group, that naturally arises investigating simple Heffter systems. Then, we show its connection with related open problems and we present some results about the validity of these conjectures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00042","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":"2026-05-18T00:42:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k0E58iYuMgBPrtY618TSHOe3yghBfdXUxiOhHEvUX6370XgT5PQ9Jlk8s+BQCpeNR51rjBpu3+dbHegh9XM4Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T10:09:38.772536Z"},"content_sha256":"191776dbf0fe16503038ffddc033541f7f5ad64d82a2f0462c26ea68620b8696","schema_version":"1.0","event_id":"sha256:191776dbf0fe16503038ffddc033541f7f5ad64d82a2f0462c26ea68620b8696"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/232SD5UD6JLMZH6HWONA7CLT35/bundle.json","state_url":"https://pith.science/pith/232SD5UD6JLMZH6HWONA7CLT35/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/232SD5UD6JLMZH6HWONA7CLT35/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":"2026-06-12T10:09:38Z","links":{"resolver":"https://pith.science/pith/232SD5UD6JLMZH6HWONA7CLT35","bundle":"https://pith.science/pith/232SD5UD6JLMZH6HWONA7CLT35/bundle.json","state":"https://pith.science/pith/232SD5UD6JLMZH6HWONA7CLT35/state.json","well_known_bundle":"https://pith.science/.well-known/pith/232SD5UD6JLMZH6HWONA7CLT35/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:232SD5UD6JLMZH6HWONA7CLT35","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":"ce274f37c008fb0ef1695f933d119a45af73d52bf6ec036188b2fa2b91df0aa3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-31T18:24:20Z","title_canon_sha256":"23864f053094c355c54adc46326386ffde99f3bb8c0f5daa501055b76f23fe65"},"schema_version":"1.0","source":{"id":"1706.00042","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00042","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00042v2","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00042","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"232SD5UD6JLM","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"232SD5UD6JLMZH6H","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"232SD5UD","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:191776dbf0fe16503038ffddc033541f7f5ad64d82a2f0462c26ea68620b8696","target":"graph","created_at":"2026-05-18T00:42:23Z","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":"In this paper we propose a conjecture concerning partial sums of an arbitrary finite subset of an abelian group, that naturally arises investigating simple Heffter systems. Then, we show its connection with related open problems and we present some results about the validity of these conjectures.","authors_text":"Anita Pasotti, Fiorenza Morini, Marco Antonio Pellegrini, Simone Costa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-31T18:24:20Z","title":"A problem on partial sums in abelian groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00042","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:f44bd5decfd1e609048d190b327fd0ec973843f084f8d6bc550ff1b3c5918feb","target":"record","created_at":"2026-05-18T00:42:23Z","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":"ce274f37c008fb0ef1695f933d119a45af73d52bf6ec036188b2fa2b91df0aa3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-31T18:24:20Z","title_canon_sha256":"23864f053094c355c54adc46326386ffde99f3bb8c0f5daa501055b76f23fe65"},"schema_version":"1.0","source":{"id":"1706.00042","kind":"arxiv","version":2}},"canonical_sha256":"d6f521f683f256cc9fc7b39a0f8973df63e5927f1d92ac3d3123a586b33e30a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6f521f683f256cc9fc7b39a0f8973df63e5927f1d92ac3d3123a586b33e30a7","first_computed_at":"2026-05-18T00:42:23.315601Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:23.315601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FpSPR8zw4z09u8gFCwyhmovIzwwOmi1O+WE8L8U6Sd4/lBKvJSNUo7ustDcfhsiajrJKT4GI71zKiPfdtjvuDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:23.316103Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.00042","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f44bd5decfd1e609048d190b327fd0ec973843f084f8d6bc550ff1b3c5918feb","sha256:191776dbf0fe16503038ffddc033541f7f5ad64d82a2f0462c26ea68620b8696"],"state_sha256":"2c6076c84e03d5ea07e5814c8ffaaccfd75b53e44fce2070be3a1df5853271ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"61vObAQE+mNVVKTOQE6Ac+UHSbVBZ9UgwURgOTlWWHLBIk/jQZCpKxHdHV8kr8SfSircH1hKGH2WgE6Z/6XdDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T10:09:38.774713Z","bundle_sha256":"9c62bd2a2eac2db2f305700f0921a03224ecbd022bbc0cb4ff3d73280842a652"}}