{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QTU2LEXIK6HEO2FAZ3RYXE5PNH","short_pith_number":"pith:QTU2LEXI","canonical_record":{"source":{"id":"1508.03231","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-08-13T14:31:46Z","cross_cats_sorted":[],"title_canon_sha256":"7802541f27ce0ecaee316bc385c0b7fa85bb2f94c164765c0ba1125b9e839433","abstract_canon_sha256":"ae7ecc2413f0c2053a105ffece0fd4e39b433e2419beeb53782e6b147258c6bc"},"schema_version":"1.0"},"canonical_sha256":"84e9a592e8578e4768a0cee38b93af69da43ff235d4f6eb349d4bd026a155a8f","source":{"kind":"arxiv","id":"1508.03231","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03231","created_at":"2026-05-18T00:46:16Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03231v2","created_at":"2026-05-18T00:46:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03231","created_at":"2026-05-18T00:46:16Z"},{"alias_kind":"pith_short_12","alias_value":"QTU2LEXIK6HE","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QTU2LEXIK6HEO2FA","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QTU2LEXI","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QTU2LEXIK6HEO2FAZ3RYXE5PNH","target":"record","payload":{"canonical_record":{"source":{"id":"1508.03231","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-08-13T14:31:46Z","cross_cats_sorted":[],"title_canon_sha256":"7802541f27ce0ecaee316bc385c0b7fa85bb2f94c164765c0ba1125b9e839433","abstract_canon_sha256":"ae7ecc2413f0c2053a105ffece0fd4e39b433e2419beeb53782e6b147258c6bc"},"schema_version":"1.0"},"canonical_sha256":"84e9a592e8578e4768a0cee38b93af69da43ff235d4f6eb349d4bd026a155a8f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:16.906664Z","signature_b64":"VUXHJQWhBhAJacBkygin/UrSL/2YiYUlY61CLbbQQOgE8f+ShyTMOE3os6f2gBftwnVD//DjUdrQWuitLJeNCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84e9a592e8578e4768a0cee38b93af69da43ff235d4f6eb349d4bd026a155a8f","last_reissued_at":"2026-05-18T00:46:16.906153Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:16.906153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.03231","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":"2026-05-18T00:46:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RN3RHy6nvlVQgjCjUgO+EgG+UIsZ2qwb1CWTDaq9snvSXuvWuPBU1vd4ICYGumRkOuBakb5O86V+g8zs5JUbBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T06:48:24.826056Z"},"content_sha256":"5f63fb2cae10ab24051788b70ac96a4d52fa191666d90fc47299889a7ca63656","schema_version":"1.0","event_id":"sha256:5f63fb2cae10ab24051788b70ac96a4d52fa191666d90fc47299889a7ca63656"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QTU2LEXIK6HEO2FAZ3RYXE5PNH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A mnemonic for the graded-case Golod-Shafarevich inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"David Anick, Warren Dicks","submitted_at":"2015-08-13T14:31:46Z","abstract_excerpt":"We draw attention to an easy-to-remember explanation for the graded-case inequality of Golod and Shafarevich. We review some of the classic material on this inequality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03231","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":"2026-05-18T00:46:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xvL1fBECkXKTEiAKXXMSW2cNbA/v929R1Li/jOBmie3enz5pfKEJlpsufFVGlODdanCeSCkdZbULObhzAQn8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T06:48:24.826416Z"},"content_sha256":"4573dc2001f7575a4a9966ff742020106705fcb881f3b5f9c66ac3ee97ca32a5","schema_version":"1.0","event_id":"sha256:4573dc2001f7575a4a9966ff742020106705fcb881f3b5f9c66ac3ee97ca32a5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QTU2LEXIK6HEO2FAZ3RYXE5PNH/bundle.json","state_url":"https://pith.science/pith/QTU2LEXIK6HEO2FAZ3RYXE5PNH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QTU2LEXIK6HEO2FAZ3RYXE5PNH/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":"2026-06-29T06:48:24Z","links":{"resolver":"https://pith.science/pith/QTU2LEXIK6HEO2FAZ3RYXE5PNH","bundle":"https://pith.science/pith/QTU2LEXIK6HEO2FAZ3RYXE5PNH/bundle.json","state":"https://pith.science/pith/QTU2LEXIK6HEO2FAZ3RYXE5PNH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QTU2LEXIK6HEO2FAZ3RYXE5PNH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QTU2LEXIK6HEO2FAZ3RYXE5PNH","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":"ae7ecc2413f0c2053a105ffece0fd4e39b433e2419beeb53782e6b147258c6bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-08-13T14:31:46Z","title_canon_sha256":"7802541f27ce0ecaee316bc385c0b7fa85bb2f94c164765c0ba1125b9e839433"},"schema_version":"1.0","source":{"id":"1508.03231","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03231","created_at":"2026-05-18T00:46:16Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03231v2","created_at":"2026-05-18T00:46:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03231","created_at":"2026-05-18T00:46:16Z"},{"alias_kind":"pith_short_12","alias_value":"QTU2LEXIK6HE","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QTU2LEXIK6HEO2FA","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QTU2LEXI","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:4573dc2001f7575a4a9966ff742020106705fcb881f3b5f9c66ac3ee97ca32a5","target":"graph","created_at":"2026-05-18T00:46:16Z","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":"We draw attention to an easy-to-remember explanation for the graded-case inequality of Golod and Shafarevich. We review some of the classic material on this inequality.","authors_text":"David Anick, Warren Dicks","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-08-13T14:31:46Z","title":"A mnemonic for the graded-case Golod-Shafarevich inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03231","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":"sha256:5f63fb2cae10ab24051788b70ac96a4d52fa191666d90fc47299889a7ca63656","target":"record","created_at":"2026-05-18T00:46:16Z","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":"ae7ecc2413f0c2053a105ffece0fd4e39b433e2419beeb53782e6b147258c6bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-08-13T14:31:46Z","title_canon_sha256":"7802541f27ce0ecaee316bc385c0b7fa85bb2f94c164765c0ba1125b9e839433"},"schema_version":"1.0","source":{"id":"1508.03231","kind":"arxiv","version":2}},"canonical_sha256":"84e9a592e8578e4768a0cee38b93af69da43ff235d4f6eb349d4bd026a155a8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84e9a592e8578e4768a0cee38b93af69da43ff235d4f6eb349d4bd026a155a8f","first_computed_at":"2026-05-18T00:46:16.906153Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:16.906153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VUXHJQWhBhAJacBkygin/UrSL/2YiYUlY61CLbbQQOgE8f+ShyTMOE3os6f2gBftwnVD//DjUdrQWuitLJeNCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:16.906664Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.03231","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f63fb2cae10ab24051788b70ac96a4d52fa191666d90fc47299889a7ca63656","sha256:4573dc2001f7575a4a9966ff742020106705fcb881f3b5f9c66ac3ee97ca32a5"],"state_sha256":"5273599fb270d4a4973ec923e46b2b343d05588df085397a5c749a76d06ec3e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fi7q5+6nd1hTjEMn+XMpQVl6DMQf8vYgOnLGx1ZdYAX3/QEGG/YjAIaOyfrmG8+Qs2Kb8/33u0f3t4fBeDL2Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T06:48:24.831543Z","bundle_sha256":"3763ae167c0e232d98c565616af63d9faeb87325f248161cc9f24ca8462ae3c0"}}